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EXPERIMENTS IN MASS EDUCATION 2000-2010

OUR STUDENTS ARE VERIFIERS OF SOLUTIONS!!!!!!


THE SOLVERS OF PROBLEMS DO NOT EXIST!!!!!!



THE GLOBAL VILL AGE HAS TAKE N OFF!!!
THE GLOBAL VILL AGE HAS TAKE N OFF!!!
THE GLOBAL VILL AGE HAS TAKE N OFF!!!
THE GLOBAL VILL AGE HAS TAKE N OFF!!!
THE GLOBAL VILL AGE HAS TAKE N OFF!!!
THE GLOBAL VILL AGE HAS TAKE N OFF!!!
THE GLOBAL VILL AGE HAS TAKE N OFF!!!
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS

THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSP ACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!


CONTEN TS

CONTEN TS

CONTEN TS

CONTEN TS

CONTEN TS

CONTEN TS

CONTEN TS

THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!




GO TO---->
PREAMBLE
CRACKING COMPETITIVE EXAMINATIONS
THE “SILVER BULLET” IN COMPETITIVE EXAMINATIONS
THE GOOD PART OF COACHNG SHOPS
THE WORLD OF MULTIPLE CHOICE EXAMINATIONS
THE WORLD OF VERIFIERS OF SOLUTIONS
THE WORLD OF SOLVERS OF PROBLEMS
THE WORLD OF COMMON SENSE AND COMPUTATION
THE WORLD OF NEGATIVE THOUGHTS AND COMPUTATION





GO TO---->

I. SOLUTIONS TO PREVIOUS GATE THEORY OF COMPUTATION PAPERS.

II. THEORY OF COMPUTATION QUESTION BANK

III. ALGORITHMS FOR GATE

IV. QUESTIONS IN LANGUAGE PROCESSORS FOR GATE

V. FAIRY TALES AND INTRACTABILITY

VI. METAMATHEMATICS FOR PRIMARY SCHOOLS

VII. METAMATHEMATICS FOR DUMMIES
VIII. ALGORITHMS FOR DUMMIES--PPTs

IX. COMPUTER SCIENCE LITERACY IN PRE-AGRARIAN AND TRIBAL SOCIETIES

X. COMPUTER SCIENCE LITERACY IN PRIMITIVE SOCIETIES

XI. DISCUSSION ON ALGORITHMS

XII. INTRACTABILITY FOR PRIMARY SCHOOLS

XIII. THEORY OF COMPUTATION MADE EASY

XIV. THEORY OF COMPUTATION FOR SECONDARY SCHOOLS

XV. PROVEN NOTES & QUESTION BANK IN THETHEORY OF COMPUTATION

XVI. SERIOUS DISCUSSION FORUM

XVII. INTRACTABILITY MADE EASY

XVIII. CRACKING COMPETITIVE EXAMINATIONS

XIX. THE “SILVER BULLET” IN COMPETITIVE EXAMINATIONS

XX. THE GOOD PART OF COACHNG SHOPS

XXI. THE BAD PART OF COACHING SHOPS

XXII. PREAMBLE TO A FORMAL STUDY OF MULTIPLE CHOICE BASED COMPETITIVE EXAMINATIONS

XXIII. THE WORLD OF MULTIPLE CHOICE BASED EXAMINATIONS

XXIV. THE WORLD OF VERIFIERS OF SOLUTIONS

XXV. THE WORLD OF SOLVERS OF PROBLEMS

XXVI. THE WORLD OF COMMON SENSE AND COMPUTATION

XXVII. THE WORLD OF NEGATIVE THOUGHTS AND COMPUTATION

XXVIII. INTRACTABILITY AND COMMON SENSE

XXIX. COMPUTER SCIENCE LITERACY IN FEUDAL SOCIETIES

XXX. COMPUTER SCIENCE LITERACY IN RURAL SOCIETIES WITH TRACES OF THE INDUSTRIAL REVOLUTION








THEORY OF COMPUTATION QUESTION BANK
PREPARED FOR DOEACC C LEVEL AND GATE
PREPARED FOR ONLINE UNIVERSITY: ecvarsity
PERIOD: 2000-2005
COMPUTER EDUCATION DIVISION
ELECTRONICS CORPORATION OF INDIA LIMITED

extension of the work 2006-2010
GATE 2009 KEY

GATE 2008 KEY

GATE 2007 KEY

PREVIOUS GATE PAPERS






THEORY OF COMPUTATION QUESTION BANK
PREPARED FOR DOEACC C LEVEL AND GATE
PREPARED FOR ONLINE UNIVERSITY: ecvarsity
USEFUL FOR CSE, IT AND MCA PROGRAMS
ALL ENGINEERING COLLEGES IN INDIA
PERIOD: 2000-2005
COMPUTER EDUCATION DIVISION
ELECTRONICS CORPORATION OF INDIA LIMITED

BANK I
BANK II
BANK III
BANK IV
BANK V
BANK VI
BANK VII
BANK VIII
BANK IX
BANK X
BANK XI
BANK XII
BANK XIII
BANK XIV
BANK XV
BANK XVI






QUALITY IN COMPUTER EDUCATION
USEFUL FOR CSE, IT AND MCA PROGRAMS
ALL ENGINEERING COLLEGES IN INDIA
M J COLLEGE OF ENGINEERING
DEPARTMENT OF CSED
(2006-2010)
THE PROOF OF THE PUDDING IS IN THE EATING

NOTES ON ALGORITHMSvisit & see--->
http://www.gateguru.org/blog

click LINK for details of POWER POINT PRESENTATIONS ON DAA FOR MOST COLLEGES IN INDIA
USEFUL FOR CSE, IT AND MCA PROGRAMS
ALL ENGINEERING COLLEGES IN INDIA
CONTACT BY e-mail
COVERS ENTIRE GATE SYLLABUS
COVER DOEACC C LEVEL










THE PROOF OF THE PUDDING IS IN THE EATING


COMMON SENSE stories giving the concept of NP-completeness------
SEE HERE: INTRACTABILITY AND COMMON SENSE









EXPERIMENTS IN LITERACY IN COMPUTER SCIENCE AND SOFTWARE ENGINEERING...... EXPERIMENTS 2006-2009.

THE PROOF OF THE PUDDING IS IN THE EATING







"The brontosaurus moved deeper into the swamps when the mammals took over the forest, but one day it ran out of swamps."


BRINGING THE THEORY OF COMPUTATION TO PRIMARY & SECONDARY SCHOOL CHILDREN ....





click here: INTRACTABILITY FOR PRIMARY SCHOOLS


THE PROOF OF THE PUDDING IS IN THE EATING















BRINGING THE THEORY OF COMPUTATION TO INTERMEDIATE STUDENTS FOR OUTSOURCING LITERACY ....

click here: STATUS OF PROJECT


THE PROOF OF THE PUDDING IS IN THE EATING


















BRINGING THE AREAS OF DATA STRUCTURES AND ALGORITHMS TO SECONDARY SCHOOL CHILDREN ....
THIS FOR PREPARING THE STUDENTS ON A MASS SCALE FOR OUTSOURCING ....
click here: EARLIER ATTEMPTS


THE PROOF OF THE PUDDING IS IN THE EATING

click here: STATUS OF PROJECT


THE PROOF OF THE PUDDING IS IN THE EATING











THEORY OF COMPUTATION QUESTION BANK
PREPARED FOR DOEACC C LEVEL AND GATE
USEFUL FOR CSE, IT AND MCA PROGRAMS
ALL ENGINEERING COLLEGES IN INDIA
PREPARED FOR ONLINE UNIVERSITY: ecvarsity
PERIOD: 2000-2005
COMPUTER EDUCATION DIVISION
ELECTRONICS CORPORATION OF INDIA LIMITED

FOR NOTES, QUESTIONS AND SOLVED PROBLEMS IN THE THEORY OF COMPUTATION. THESE PROBLEMS HAVE BEEN USED FOR ABOUT A DECADE WITH PROVEN GATE RESULTS. THE DOCUMENT HAS SOME TYPOGRAPHICAL ERRORS WHICH HAVE TO BE CORRECTED.
CONTENTS
FINITE AUTOMATA & REGULAR SETS** CONTEXT FREE LANGUAGES & PUSH DOWN AUTOMATA** CONTEXT FREE LANGUAGES & PUSH DOWN AUTOMATA(CONTD)** FINITE AUTOMATA & REGULAR SETS(CONTD)** TURING MACHINES AND R.E. SETS** INTRACTABILITY MADE EASY** REGULAR EXPRESSIONS** FINITE AUTOMATA WITH MOVES ON THE EMPTY STRING** NONDETERMINISM & FINITE AUTOMATA** THE FINITE AUTOMATA—AN EXAMPLE** KLEENE’S THEOREM** TOP DOWN DETERMINISTIC PARSING—AN EXAMPLE** TOP DOWN DETERMINISTIC PARSING—A DETAILED EXAMPLE** BOTTOM UP PARSING WITHOUT LOOKAHEAD
CLICK HERE-----> FOR DISCUSSION OF PROBLEMS
(only if you seriously interested).

THE PROOF OF THE PUDDING IS IN THE EATING







CLICK HERE FOR AN ATTEMPTED COMMONSENSE EXPLANATION OF INTRACTABILITY. visit & see--> http://www.gateguru.org/blog
FOR FREE DISCUSSION

THE PROOF OF THE PUDDING IS IN THE EATING
















COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS

COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS R U LE!!









GO TO---->
PREAMBLE
CRACKING COMPETITIVE EXAMINATIONS
THE “SILVER BULLET” IN COMPETITIVE EXAMINATIONS
THE GOOD PART OF COACHNG SHOPS
THE WORLD OF MULTIPLE CHOICE EXAMINATIONS
THE WORLD OF VERIFIERS OF SOLUTIONS
THE WORLD OF SOLVERS OF PROBLEMS
THE WORLD OF COMMON SENSE AND COMPUTATION
THE WORLD OF NEGATIVE THOUGHTS AND COMPUTATION



DRAFT

EXPERIMENTS WITH THE SILVER BULLET FOR CRACKING COMPETITIVE EXAMINATIONS






INTRODUCTION


Any fiercely sought after success by a very large body of students in a competitive examination becomes a social event. This will naturally have positive savory aspects and also negative unsavory aspects. The example of the GATE examination is taken. Experiments were conducted for about a decade to test out a directive from Prof. C A R Hoare, of Oxford, when he visited India. He suggested that one should search for COMMON SENSE explanations in the study and exposition of concepts and principles in engineering and science. The experiments spanning a decade were conducted in real life. They involved the direct training/coaching of a couple of thousand students to tackle GATE in a few conceptually challenging and difficult subject areas, with hundreds of success stories and observing firsthand the progress of about half a lakh aspiring students in a spectrum of subject areas, again with hundreds of success stories. No entry level screening of the students was done except for the requirement that they were bonafide students in the third or fourth year of undergraduate engineering education. Recently qualified students awaiting employment, some postgraduate students and a sprinkling of engineering college faculty were also part of the audience. They spanned a large spectrum of intellectual capability from the mediocre to excellent. Their entry level technical preparation for the experiments spanned a wide spectrum from very poor to very good. Based on the success story a savory technical model is outlined for aspiring students and GATE shops. The unsavory behind the scenes activities the business model involves and threats looming on the horizon are then outlined for general social consumption.


OUR STUDENTS ARE VERIFIERS OF SOLUTIONS!!!!!!


THE SOLVER OF PROBLEMS DOES NOT EXIST!!!!!!







COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS

THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !




PART I : THE PROPHECIES OF SUCCESS
GATE: SOARING TO THE CLOUDS
THE GATE SHOP: TECHNICAL MODEL
CRACKING GATE: THE SILVER BULLET
GENERALISING THE SILVER BULLET
TECHNICALLY AUDITING A GATE SHOP

PART II: THE PROPHECIES OF DOOM
GATE: PLUNGING TO THE DEPTHS
THE OUTSOURCING SCENARIO
GATE AND OUTSOURCING
THE GATE SHOP: BUSINESS MODEL
THE GATE SHOP: BUSINESS MODEL REVISITED
REJUVENATING GATE







COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS





PART I

FOR THE ASPIRING STUDENT: THE SAVOURY PATH TO SUCCESS
”It was the best of times…..We are all going direct to heaven……”




For NIL circulation.




GATE: SOARING TO THE CLOUDS
Over the last half a century the Tier I engineering educational institutions in India. viz., the older IITs and IISc have managed to elevate themselves to the enviable pedestal of not being subject to scrutiny, or being answerable or accountable to any temporal or spiritual agency or authority.
One of the lesser jewels in their crown, to protect their exclusive world, has been the GATE examination which screens and determines entry level aspirants for postgraduate engineering education in a sizable number of higher tier institutions. Incidentally this examination is also used by the Government of India for screening and entry level qualification to some prestigious R&D institutions.
Since its low standard at the time of its inception it had steadily improved as the demand and credibility for it grew.





THE GATE SHOP: TECHNICAL MODEL
The GATE examination syllabus is pompously large and forbidding. It has varied over the last two decades of the GATE examination with the same pompous characteristics. A student contemplating this syllabus and its variations in his/her area of interest stands in awe and fear as when beholding Goliath in all his arrogance. Unsuccessful GATE shops have tried to cover as much of the syllabus as they could by the formal instructional process. They found that an imaginary number of students were successful. They closed down. The student could not combat Goliath. The student has to be converted to a David. The catapult has to be found.
Successful GATE shops followed a more agile method that directly considers the questions in the examinations. GATE is a very young examination. It is hardly two decades old. The entire legacy of previous question papers is easily available in any urban college bookshop.
A comprehensive study is made in an area of all the questions in all the previous papers, with each question being cursorily studied for classification purposes. The study only takes an intense effort of 3-4 days as the database is tiny. A coarse first level classification of the questions based on subjects is made. Then in the second pass over the questions a fine grained classification is made as per the topic in the subject. A simple pattern emerges. The questions cluster around a small number of narrow topics. Standard questions from standard text books, either copied verbatim or used with small variations abound. Repetitions, variations and metamorphoses of problems are plenty. A clear pattern emerges on the strengths and weaknesses, likes and dislikes, favorite topics and texts in the collective wisdom of the paper setters and examiners. Third and subsequent passes over the entire set of questions help in the identification of the concepts and principles that recur in the question papers.
The student only has to repeatedly study or be instructed in the collection of topics the syllabus has reduced to. This can be done either from the subject point of view or alternatively the subject as defined by fuzzy solution areas to the collection of legacy questions. A reverse mapping from the questions is like a bunch of fixed spotlights on a subject. Only the bright patches need be considered. Goliath has collapsed.




CRACKING GATE: THE SILVER BULLET
Coming back to the technical model, repeated study of a topic alone may not usually obtain the answer to a GATE question. The question may have twists. Approximate solutions are of no use. High quality approaches to the solutions and actual solutions of the legacy questions are required. The narrow collection of topics now reduces to GATE questions with twists. Goliath has been replaced by a pack of baby werewolves, and legend has it that a werewolf can only be destroyed with a silver bullet.
Successful GATE shops first instruct the student in the isolated narrow collection of topics. When the student comes of age, the initiation into the mantra for the silver bullet takes place, along with solutions to legacy question papers.
The GATE shops finally impart the hallowed instruction in the silver bullet for the GATE examination: the method of elimination for multiple choice questions. This silver bullet has a great deal in common with Simulation studies, as noted by Prof. C. A. R. Hoare. It rigorously trains the student how to determine what is not in the subject rather than knowing what is in the subject. The student becomes an expert in determining the wrong answers.
The silver bullet has interesting properties. Like the plutonium in a fast breeder nuclear reactor it can grow by repeated use in size, power and effectiveness. It is first applied to a motley collection of questions from guides, question banks and mock test question papers which are in the public domain and given by GATE shops. The beauty is that the though these may be of dubious quality the silver bullet grows in power with each question regardless of its correctness, quality or level of difficulty. The it is brought up to the critical mass by applying it to a collection of real problems chosen from a reasonable sample of previous GATE papers, all of which are in the public domain. Then at its critical mass it is applied by the student in the final examination.
The net result the GATE shops and students is to magically and effectively swamp not only their pockets but also incidentally the IITs and other institutions that give credence to the GATE score. All this thanks to the fact that the GATE examination has steadily become easier over the years.
High quality of faculty helps but is not essential in the development of the silver bullet. The students can sincerely work in pairs or small motivated self-organizing teams. They should have a very patient average quality faculty member or some team member who plays the role with whom they can verbalize their attempted solutions. This also ensures growth of the silver bullet.
One of the important properties of the silver bullet is that it ensures the growth in the quality of the faculty also for coaching purposes. The faculty member degenerates to cycle shop faculty level and becomes an expert in instructing even mediocre students in techniques for guessing and/or determining the wrong answers.
The silver bullet does not work for all questions. GATE 2003 is uniformly fecund in questions that are resistant to the silver bullet. However it also has a sizable number of questions, some of them pompously forbidding, that are easily susceptible to it.




GENERALISING THE SILVER BULLET
The silver bullet can be applied as a general rule to any competitive examination in any discipline, in any subject, in any language, in any culture and in any situation, where the questions are in the multiple choice format. It works best if a database of real life questions exists in the public domain. However, regardless of the quality of the question the silver bullet will grow in power with use. Thus it can even be used with some notable success in the GRE & TOEFL examinations where the real questions are ostensibly in the private domain, but a data warehouse of questions of mixed quality exists internationally in the public and grey markets, and with the student community. It can generally be used for competitive examinations determining entrance to Business Schools the world over. It can be applied to some international entrance examinations for undergraduate studies in educational institutions in various countries. However in the undergraduate entrance examination for Tier I institutions in India it can only be applied for superior results by students who possess both breadth and depth of knowledge across the prescribed syllabus. If care is not taken to shield the questions from the silver bullet the examination standard and results can degenerate as in GATE.
When competitive examinations based on the multiple choice examination exist, agencies of all types of respectability, from all walks of life, come forward with mock tests and examinations which may be either offline or online. They are either at cost or ostensibly free and social service oriented, but basically after the associated publicity. Guides at various levels of quality exist for any competitive examination. The concept of the silver bullet shows that both mock tests and guides are all useful in developing the power of the silver bullet. However, to bring it to its critical mass a collection of real life questions, possibly drawn from legacy question papers, is essential. Relying on legacy question papers is essentially playing the dangerous game of extrapolation. We are trying to predict the future. However, the student is interested only in the next examination and the time frame for that is almost immediately in the future. This allows extrapolation to be successfully used.
It many be mentioned in passing that application of the silver bullet is akin to the eternal fable of the six blind men and the elephant.
Let us consider our friend and model student David whom we met some time ago. We arm him with the catapult and he destroys Goliath. When Goliath transformed himself into a pack of werewolves he attacked them with the silver bullet. Then he grew the silver bullet in size till it reached its critical mass, like a large lump of plutonium, and he blasted the GATE examination. Now we will let David apply the silver bullet to TOEFL and obtain a great score. Unlike some leading Oxford dons who with a straight face tolerate all ex-colonial English, on which incidentally the sun does not set, some people give weight age to TOEFL. Now with David's score in TOEFL we cannot say David knows English. It is however guaranteed that he is an expert in knowing what is not English. This does not normally happen as TOEFL is a well planned examination
TECHNICALLY AUDITING A GATE SHOP
The properties of the silver bullet shows that the public and student have a tool to audit a GATE shop or a shop claiming to give instruction/coaching for a competitive examination. A student, even if of mediocre capability, should effectively be able to solve a randomly selected sample of legacy questions, if the coaching/training is effective. An audit of the faculty labor is the extent to which they can solve and impart instruction to the student in confidently and correctly solving the legacy question papers.



COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS





OUR STUDENTS ARE VERIFIERS OF SOLUTIONS!!!!!!


THE SOLVER OF PROBLEMS DOES NOT EXIST!!!!!!







COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS

THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !




PART II

FOR SOCIETY: THE UNSAVOURY PATH TO FAILURE
”....it was the worst of times…..we are all going direct the other way……”








GATE AND THE PROBLEM WITH IT
Over the last ten years, barring perhaps 2003 A.D., the standard of the GATE examination has rapidly plummeted down. It has become easier over the years to qualify in GATE. The reasons for the fall in the standard are conjectured below.
This perhaps is in line with the steady degeneration witnessed in most engineering education over the last decade in India. This education now seems more oriented towards turning out cheap semi-skilled labour, on a mass scale, as a national herd mentality movement.




THE OUTSOURCING SCENARIO
All the educational process is for catering to the oversold and over hyped chimera of the uncertain, internationally highly competitive, outsourced IT (& progressively other areas) market of the high wage countries. The major hype is oriented especially to the SWITCH(1) group of companies and the MNC development centers, and the long tail of the IT outsourcing industry. This ignores the fact that most of the work of IT-labour and in general all outsourcing labour, are in the lower level activities of the software life cycle and the business process, respectively. The aura is with the fascinating bubble of easy money (by local economic standards) and its associated lifestyle from the seemingly endless bubble of progressively lucrative job and wage advancement and opportunities. We seem to have forgotten the competition from the Third Word and the other BRIC(2) countries forming as storm clouds on the horizon. They will do the same work at much more economical rates. Perhaps even an order of magnitude lower than now may be the difference in wages and burdened costs, in the not too distant future, as the Global Village fully dawns upon the Third World(3). As a case in point consider the Olympics opening & closing ceremony, as to what would happen if the vast, untapped, economically backward, intellectually competent, deep interiors of the Third World are plummeted into the Global Village and outsourcing market(4).




GATE AND OUTSOURCING
It is an interesting and ludicrous situation that we can have a valid thesis that for over a decade the quality of the GATE examination and the demand for the same from the student community, varies inversely with the quantity of demand for IT-labour and outsourcing labour made by the high wage countries on India.
The rise of the GATE standard, a radical increase in the demand for the GATE examination by aspiring students and a mushrooming of GATE coaching institutions, was noticed when there was a major slump in the demand for IT-labour after the Y2K boom in India, and the almost simultaneously occurring dot com bust in the Silicon Valley.
The downfall of the GATE standard, and collapse of many coaching institutes whose business model was cash over content, was witnessed steadily in pace with the exponential growth of the outsourcing opportunities over the last five years, with the GATE 2008 question papers being uniformly fecund with bloomers.
Now in 2008 A.D., at the height of the demand for IT-labour, coaching institutions which survived the crash were those that invested in some semblance of content plus cash. The GATE examination quality is now at a low ebb. It is just the variation and metamorphosis of a standard bagful of questions on a narrow spectrum of selected topics. In recent question papers a sufficiently large bulk of questions, to ensure glorious success, can be easily and rapidly solved, by suitably instructed mediocre students, using a standard collection of tricks, methods, techniques and stunts applied using a definite process.




THE GATE SHOPS: BUSINESS MODEL
GATE coaching shops have developed to take advantage of this situation. They follow the proven tradition and business model that most commercial training and coaching institutions have followed in India. This business paradigm peaked during the national bubble of the computer software training era. This when computers were either nonexistent or notoriously scarce commodities. Real know-how, in industrial strength IT of the high wage countries, was little or nonexistent. This was both in the public and private sectors and the gold rush was on. The gold rush was evidently initially created by the high wage countries when contemplating the cost of maintaining their stockpile of legacy software. The next gold rushes were the Y2K problem, the labor for the dot com boom and the international outsourcing movement.
During the Y2K bubble hordes of persons, paying exorbitant fees, were trained on the IBM mainframe, without anyone involved having a ghost of an idea as to what the mainframe was all about. Certified poor souls who rushed off to the high wage countries after the training were actually trained by some kind souls there.
During the IT training bubble of the nineties, a little bit of programming instruction augmented by a little bit of IT knowledge was taken. This was encapsulated in a lifestyle of consumerism that liberalization and globalization made possible. The sugary encapsulated product along with unlimited and round the clock access to the personal computer was the product marketed with a lot of hype by training shops and sold to hordes of people at enormous cost.
The pattern followed by the GATE shops is by now a very familiar story. It was developed over the last three decades. The pattern, it is emphasized, was in a vacuum of knowledge in the industrial strength IT of high wage countries. This pattern applies to most software training attempts by small, medium or large shops, businesses or corporations, whether in the private or public sector. The pattern was and is even today some sort of a national industrial disease and applies to all the actors. However it makes proven sound marketing sense in all the businesses. The shops following the pattern charge exorbitant fees, an order of magnitude more than what is reasonable. They are ostensibly backed and/or staffed by noted personalities, dormant educationists, leading social service and government organizations of impeccable standing and have exclusive access to imaginary high quality experienced industry professionals, and noted faculty of the higher tier educational institutions. They ostensibly have shortly to be formalized links with leading or reputed national and international educational institutions for faculty and accreditation. They claim that with their proven expertise and experience, and in accordance with the near wishes of their heart, and a lifetime aim, their shops will shortly spawn formal educational institutions of repute, in the memory of a near departed soul. This is the only reason why these noble souls are forced with great reluctance to accept money from the students as fees. If very successful they all at the end of their boom period enter the commercial education racket in formal education. They expend enormous time and energy in both free and paid manipulated gaudy publicity in all forums, public places and media. They have lists of real &/or manipulated &/or imaginary performance in previous years in terms of rank holders. They have a small library of easily available text books. In some business cases of large corporations the students are ostensibly free to use the inaccessible large corporate library and profit form the guidance of an inaccessible large corporate pool of technical specialists. These are needless to say imaginary promises. They are well stocked with shoddy student created subject notes and innocently crude mock question papers and question banks. They have a reliable set of minions, who are rigidly controlled wage slaves, for all the umbrella activities of running the show. They have sharp cash based accounting practices common to the grey market if in the small and medium private sector. In the public sector and large private sectors they have sharp accounting practices to bypass the internal and external audit systems. They coolly let drop some the names of their ex-students or ex-employees, who they claim have gone to the high wage countries. They claim that these ex-students and ex-employees are among the crown jewels of MNCs. They flaunt the address of a motel in some high wage country and claim it is their international office for their shortly exploding international IT activities. They all claim to be dedicated social workers and philanthropists, with mindsets far above the concept of gain and make no mention of the bulging sacks of hard cash hidden away in their gowdowns. A crucial difficulty large training and coaching shops, with exploding business, have always had is to acquire a permanent premises, either in their name or in benami names, either registered or notarized, without which they are easily subject to blackmail. As per of the business model they all strive very hard to convert their faculty to wage slaves or economic control/dependence. In most training and coaching centers controlled and run by the private or franchised by the public sectors standard complaints by partners, faculty and staff are made in connection with the attempts to renege on promises made with respect to monies payable.
In the business model, the GATE shops, like the software training shops and all coaching shops, have smooth talking consultants. These persons either implicitly use the projected image of the shop/institution or explicitly brainwash the raw material of the ever optimistic, eternally easily gullible and believing, eager, wide eyed, young students to an imaginary virtual world of promised instructional excellence, vast knowledge impartation & assimilation, regular tests truly reflecting the unknown real question paper coming after the training period is over and guaranteed rosy cheeks when they will ultimately see their GATE examination results.
The aim is to make the student part with the cash and for this any story or promise is in order. In reality, just like the commercial software training attempts by teaching shops and even large and reputed public and private sector institutions, they use precocious students & GATE qualified ex-students, at low wages, as faculty. They use, at more reasonable wages, augmented cycle shop quality histrionic faculty. The collect the students in herds with some sound systems and semblance of teaching aids.
Some GATE shops have no technical model. They take the business risk of collecting a crowd of students, imparting some instruction and relying on luck. Hopefully some bright students should exist in a crowd who will obtain ranks in GATE. This relies on the random distribution of brightness in the student community. This success, if it occurs, will justify the business process of the GATE shop and allow it to grow. Such shops have not gone far. A technical model is needed and successful GATE shops have a well developed model.




THE GATE SHOPS: BUSINESS MODEL REVISTED
In the teething period the GATE shop may require the stick and multiple carrot approach with respect to faculty to aid the isolation of the topics in any particular area and some semblance of solutions to the legacy GATE question papers. This is a usual feature in the business model of the training and coaching institutions. Once the topics are isolated, shoddy notes created on them and the know-how in approximate solutions of low quality to the legacy question papers is gained, the faculty are replaced by ex-students as faculty at a fraction of the wages.
This allows the GATE shop to build a reusable standard model of a shop. Then it can diversify into branches in various urban areas in the country. Some have done this at the height of the demand for GATE from the student community.
There is however a great drawback in that the system has a flaw. It is not so easy to solve the entire set of legacy questions without a couple of years of experience in the subject or sustained in-depth effort. Alternatively the student has to put in sustained effort in the solution spots highlighted by a reverse mapping from the legacy questions. Mastery of the principles is essential. It is a one thing to solve all the questions and a completely different matter to instruct a mediocre student to do it unilaterally. The training in the silver bullet is essential.
Some GATE shops which avoided paying the faculty their dues wound up very easily, and vanished in smoke. Some GATE shops which overpaid their faculty with liberal fat advances ended up in the tax collectors vision. The eternal problem in the coaching industry is the management of the compensation to the faculty, it should not be low and at the same time it should not be high.




REJUVENATING GATE
The fluctuation in the GATE standard has to be attended to. Continued success in the GATE examination over the last few years in coaching mediocre students by the hundreds shows a negative trend in the standard. It is high time the older IITs & IISc stop unilaterally blaming the sharp business acumen oriented GATE shops, which in their own way and style do a social service. They should wake up like Kumbhakarna on their somnolescent pedestals. They should restructure their GATE syllabus. The should put in some dedicated time and effort to redo the content and standard of the GATE examination. In standard of evaluation it should be invariant with respect to whatever geometric spaces the IT-labour and other outsourcing labour demands from the high wage countries may be in. They should bring it to the lines of respectability that the entrance examination for undergraduate studies has always commanded.


COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS

NOTES:-
(1)SWITCH---Satyam, Wipro, Infosys, TCS, Cognizant and HCL. These companies are among the few that have mastered the art of maintaining large software. This is not everybody's cup of tea. Small and medium companies that tried the game have failed. However, the hard work ethic and sharp business practices these companies have followed to acquire the know-how by hook or by crook, can possibly be rapidly replicated by some other determined low wage country or environment, even if starting with zero IT know-how.
(2)BRIC---Brazil, Russia, India and China. Wages of US$70K per year for a job in a high wage country translates in outsourcing to a job with wages of INR Rs.60,000/- per month in India and the BRIC countries.
(3)During the aftermath of the dot com bust and preceding the outsourcing boom wages of INR RS.5,000/- to Rs.10,000/- per month were considered to be good in the secondary IT industry. In such a situation the consumerist lifestyle has to be abandoned or radically curtailed.
(4)The vast interiors of India are still not in the Global Village. However, the cell phone seems to have however penetrated into the deep interiors.

OUR STUDENTS ARE VERIFIERS OF SOLUTIONS!!!!!!

THE SOLVERS OF PROBLEMSDONOT EXIST!!!!!!






GO TO---->
PREAMBLE
CRACKING COMPETITIVE EXAMINATIONS
THE “SILVER BULLET” IN COMPETITIVE EXAMINATIONS
THE GOOD PART OF COACHNG SHOPS
THE WORLD OF MULTIPLE CHOICE EXAMINATIONS
THE WORLD OF VERIFIERS OF SOLUTIONS
THE WORLD OF SOLVERS OF PROBLEMS
THE WORLD OF COMMON SENSE AND COMPUTATION
THE WORLD OF NEGATIVE THOUGHTS AND COMPUTATION





GO TO---->

I. SOLUTIONS TO PREVIOUS GATE THEORY OF COMPUTATION PAPERS.

II. THEORY OF COMPUTATION QUESTION BANK

III. ALGORITHMS FOR GATE

IV. QUESTIONS IN LANGUAGE PROCESSORS FOR GATE

V. FAIRY TALES AND INTRACTABILITY

VI. METAMATHEMATICS FOR PRIMARY SCHOOLS

VII. METAMATHEMATICS FOR DUMMIES
VIII. ALGORITHMS FOR DUMMIES--PPTs

IX. COMPUTER SCIENCE LITERACY IN PRE-AGRARIAN AND TRIBAL SOCIETIES

X. COMPUTER SCIENCE LITERACY IN PRIMITIVE SOCIETIES

XI. DISCUSSION ON ALGORITHMS

XII. INTRACTABILITY FOR PRIMARY SCHOOLS

XIII. THEORY OF COMPUTATION MADE EASY

XIV. THEORY OF COMPUTATION FOR SECONDARY SCHOOLS

XV. PROVEN NOTES & QUESTION BANK IN THETHEORY OF COMPUTATION

XVI. SERIOUS DISCUSSION FORUM

XVII. INTRACTABILITY MADE EASY

XVIII. CRACKING COMPETITIVE EXAMINATIONS

XIX. THE “SILVER BULLET” IN COMPETITIVE EXAMINATIONS

XX. THE GOOD PART OF COACHNG SHOPS

XXI. THE BAD PART OF COACHING SHOPS

XXII. PREAMBLE TO A FORMAL STUDY OF MULTIPLE CHOICE BASED COMPETITIVE EXAMINATIONS

XXIII. THE WORLD OF MULTIPLE CHOICE BASED EXAMINATIONS

XXIV. THE WORLD OF VERIFIERS OF SOLUTIONS

XXV. THE WORLD OF SOLVERS OF PROBLEMS

XXVI. THE WORLD OF COMMON SENSE AND COMPUTATION

XXVII. THE WORLD OF NEGATIVE THOUGHTS AND COMPUTATION

XXVIII. INTRACTABILITY AND COMMON SENSE

XXIX. COMPUTER SCIENCE LITERACY IN FEUDAL SOCIETIES

XXX. COMPUTER SCIENCE LITERACY IN RURAL SOCIETIES WITH TRACES OF THE INDUSTRIAL REVOLUTION






COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS

THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!!

(draft-----stray thoughts)**(circa 2009----2011)
(M J COLLEGE, HYDERABAD)


VANITY FAIR REVISITED
VANITY FAIR REVISITED
VANITY FAIR REVISITED
VANITY FAIR REVISITED
VANITY FAIR REVISITED
VANITY FAIR REVISITED
VANITY FAIR REVISITED


OR


COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS

(A PROCUSTEAN AP PLICATION TO OUTSOURCING)

WITH

UBIQ UITO US COMPUTATI ON IN THE MEMEX- AIDED GLOBAL VILLAGE
UBIQ UITO US COMPUTATI ON IN THE MEMEX- AIDED GLOBAL VILLAGE
UBIQ UITO US COMPUTATI ON IN THE MEMEX- AIDED GLOBAL VILLAGE
UBIQ UITO US COMPUTATI ON IN THE MEMEX- AIDED GLOBAL VILLAGE
UBIQ UITO US COMPUTATI ON IN THE MEMEX- AIDED GLOBAL VILLAGE
UBIQ UITO US COMPUTATI ON IN THE MEMEX- AIDED GLOBAL VILLAGE
UBIQ UITO US COMPUTATI ON IN THE MEMEX- AIDED GLOBAL VILLAGE

( [I NTERACTIVE] VE RIFIERS, SOLVERS)


WITH

{[( COMMON SENSE RENDERING ATT EMPTED)]}
{[( COMMON SENSE RENDERING ATT EMPTED)]}
{[( COMMON SENSE RENDERING ATT EMPTED)]}
{[( COMMON SENSE RENDERING ATT EMPTED)]}
{[( COMMON SENSE RENDERING ATT EMPTED)]}
{[( COMMON SENSE RENDERING ATT EMPTED)]}
{[( COMMON SENSE RENDERING ATT EMPTED)]}

(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)



CONTEN TS


PART ?O?: P RE AMBLE
PART I: S TU DY AREA
PART II: V ER IFIERS
PART III: S OL VERS
PART IV: C OMMON SENS E
PART V: THE UNP AL ATABLE

(WITH DUE APOLOG IES TO THE FORMALISERS & OVE R - FORMALISERS)
( THE PROOF OF THE PUDDING IS
IN THE EATING)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)


CONTEN TS

PREAMBLE
THE WORLD OF MULTIPLE CHOICE EXAMINATIONS
THE WORLD OF VERIFIERS OF SOLUTIONS
THE WORLD OF SOLVERS OF PROBLEMS
THE WORLD OF COMMON SENSE AND COMPUTATION
THE WORLD OF NEGATIVE THOUGHTS AND COMPUTATION





PART ?0?
PREAMBLE


Stray thoughts to experiment with COMMON SENSE explanations of Computer Science and Software Engineering by me to myself.

Stray thoughts for you, dear reader, to experiment with COMMON SENSE explanations of Computer Science & Software Engineering by you to yourself.

START OF STRAY THOUGHTS

[I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS!




PART I
THE WORLD OF MULTIPLE CHOICE BASED EXAMINATIONS





CONTEN TS

PROLOGUE
THE SCOPE OF THE PROBLEM OF MULTIPLE CHOICE BASED EXAMINATIONS
THE EXTENDED SCOPE OF THE PROBLEM OF MULTIPLE CHOICE EXAMINATIONS
THE FURTHER EXTENDED SCOPE OF THE PROBLEM OF MULTIPLE CHOICE EXAMINATIONS
THE MODEL TO STUDY MULTIPLE CHOICE BASED EXAMINATIONS
THE CONCLUSION ATTEMPTED FROM THE STUDY
THE RESTRICTIONS USED IN THE STUDY
THE STRATEGY FOLLOWED IN THE STUDY
ARGUMENT I--BASED ON THE INFORMATION CONTENT OF THE QUESTION
ARGUMENT II--BASED ON HIERARCHIES OF COMPLEXITY CLASSES
THE ANNOTATIONS USED IN PSEUDO-VENN DIAGRAMS
CHARACTERISTICS OF PSEUDO-VENN DIAGRAMS-I
CHARACTERISTICS OF PSEUDO-VENN DIAGRAMS-II
THE USE OF THE PSEUDO-VENN DIAGRAMS
THE USE OF THE DIAGRAMS ELSEWHERE
THE SCOPE OF THE DIAGRAMS
ARGUMENT III--ON THE EXISTENCE OF EASY CHOICES TO A QUESTION
THE EXPLANATION ATTEMPTED
ARGUMENT III--THE EFFECT OF THE INTERSECTION OPERATION
THE JUSTIFICATION FOR THE EFFECT OF INTERSECTION
THE JUSTIFICATION BY PATTERN MATCHING
THE POSSIBLE AND USUAL EXISTENCE OF EASY COMPLEMENTS TO A PROBLEM
COMMON SENSE DEMONSTRATION OF THE USE OF THE COMPLEMENT
THE DIFFICULTY OF FAULT FINDING
ARGUMENT V-AN INFORMAL INTRODUCTION TO NONDETERMINISM
THE EXPRESSIVE POWER OF NONDETERMINISM-I
THE EXPRESSIVE POWER OF NONDETERMINISM-II
THE EXPRESSIVE POWER OF NONDETERMINISM-III
ARGUMENT VI--THE LARGE USEFUL CLASS OF SEEMINGLY INTRACTABLE PROBLEMS
THE EXPRESSIVE POWER OF NONDETERMINISM-IV
THE EXPRESSIVE POWER OF NONDETERMINISM-V
THE EXPRESSIVE POWER OF NONDETERMINISM-VI
ARGUMENT VII--THE SUM OF SUBSETS PROBLEM AS AN EXAMPLE
A PROBLEM OF INTEREST --- THE HAMILTONIAN PATH DETERMINATION
A PROBLEM OF INTEREST --- THE NODE COVER PROBLEM
A PROBLEM OF INTEREST -- THE BIN PACKING PROBLEM
ARGUMENT VIII--THE IMPORTANCE OF CONCURRENT THINKING
THE IMPLEMENTATION OF CONCURRENCY-I
THE IMPLEMENTATION OF CONCURRENCY-II
NONDETERMINISTIC THINKING--I
NONDETERMINISTIC THINKING--II
THE DEPTH OF SEARCH REQUIRED IN NONDETERMINISTIC THINKING
THE WELL BEHAVED FUNCTIONS
THE WEAKNESS OF WELL BEHAVED FUNCTIONS--I
THE WEAKNESS OF WELL BEHAVED FUNCTIONS--II
THE WEAKNESS OF WELL BEHAVED FUNCTIONS--III
THE WEAKNESS OF WELL BEHAVED FUNCTIONS--IV
THE WEAKNESS OF WELL BEHAVED FUNCTIONS--V
TACKLING HOMOMORPHISM--I
TACKLING HOMOMORPHISM--II
TACKLING HOMOMORPHISM--III
TACKLING THE METAMORPHOSES OF SPECIFICATIONS-I
TACKLING THE METAMORPHOSES OF SPECIFICATIONS-II
TACKLING THE METAMORPHOSES OF SPECIFICATIONS-III
TACKLING THE METAMORPHOSES OF SPECIFICATIONS-IV
TACKLING THE METAMORPHOSES OF SPECIFICATIONS-V
TACKLING THE METAMORPHOSES OF SPECIFICATIONS-VI
TACKLING THE METAMORPHOSES OF SPECIFICATIONS-VII
TACKLING THE METAMORPHOSES OF SPECIFICATIONS-VIII
TACKLING THE METAMORPHOSES OF SPECIFICATIONS-IX
TACKLING THE EFFECTS OF MISREADING A QUESTION-I
TACKLING THE EFFECTS OF MISREADING A QUESTION-II
TACKLING THE EFFECTS OF MISREADING A QUESTION-III
TACKLING THE EFFECTS OF MISREADING A QUESTION-IV
ARGUMENT XI--THE ANALYSIS OF ALGORITHMS
TACKLING ALGORITHMS--I TO XVI
ARGUMENT XII--MISREADING THE QUESTION
THE MODEL FOR MISREADING A QUESTION
A FORMAL MODEL FOR MISREADING A QUESTION
THE DANGERS OF MISREADING A QUESTION-I
THE DANGERS OF MISREADING A QUESTION-II
THE DANGERS OF MISREADING A QUESTION-III
COMMONSENSE AND THE EFFECTS OF MISREADING A QUESTION-I
COMMONSENSE AND THE EFFECTS OF MISREADING A QUESTION-II
WELL-FORMED QUESTIONS
ILL-FORMED QUESTIONS
STANDARD EXAMINATIONS BASED ON THE MULTIPLE CHOICE PATTERN
NON-STANDARD EXAMINATIONS BASED ON THE MULTIPLE CHOICE PATTERN
THE ASSUMPTIONS OF STANDARD EXAMINATIONS
A FOLK THEOREM BASED ON EXPERIENCE
JUSTIFICATION OF THE FOLK THEOREM-I
JUSTIFICATION OF THE FOLK THEOREM-I
THE CONSULTANT IN REAL LIFE
THE REGULAR CLASSES AS CONSULTANTS IN COMPUTATIONAL COMPLEXITY
THE PROOF FINDING METHODS-I: THE PIGEON HOLE PRINCIPLE
THE PROOF FINDING METHODS-II: THE SLIDING WINDOW
PUMPING ON WHAT IS SEEN THROUGH A SLIDING WINDOW
THE PROOF FINDING METHODS-III: MATHEMATICAL INDUCTION
THE PROOF FINDING METHODS-IV: PROOF BY CONTRADICTION
THE PROOF FINDING METHODS-V: THE PART VS THE WHOLE
THE USE OF THE RELATIONSHIP BETWEEN THE PART AND THE WHOLE
THE PROOF FINDING METHODS-VI: OTHER PROOF FINDING TECHNIQUES
THE PROOF FINDING METHODS-VII: PROVING WRONG CHOICES
THE PROOF FINDING METHODS-VIII: USING CONCURRENCY, NONDERTERMINISM & ALTERNATION
THE PROOF FINDING METHODS IX: USE OF PROBABILITY AS A STRATEGY
THE PROOF FINDING METHODS X: INTERACTIVE VERIFIERS & SOLVERS
THE PROOF FINDING METHODS XI: THE IP=PSPACE MODEL
TWO GENERAL TECHNIQUES--'DEFORMALISATION' AND 'INSTANTIATION'
THE USE OF 'VERBALISATION'
THE USE AND WEAKNESS OF GENERALISATIONS
EXPLOITING GENERALISATION
DEFORMALISATION
INSTANTIATION
REFORMALISATION
DEMONSTRATION I--THE USE OF 'VERBALISATION', 'DEFORMALISATION' & 'INSTANTIATION'
AN APPLICATION TO CONCEPTS IN CONCURRENT COMPUTATION
DEMONSTRATION II--THE USE OF 'VERBALISATION', 'DEFORMALISATION' & 'INSTANTIATION'
THE CONCEPT OF UNDECIDABILITY EXPLAINED
THE DECIDABILITY OF PARTIAL DECIDABILITY
DEMONSTRATION III--THE USE OF 'VERBALISATION', 'DEFORMALISATION' & 'INSTANTIATION'
DEMONSTRATION IV--THE USE OF 'VERBALISATION', 'DEFORMALISATION' & 'INSTANTIATION'
NP-COMPLETENESS AND COMMON SENSE
NP-COMPLETENESS DEMYSTIFIED--I TO VII
OTHER APPLICATIONS OF COMPUTATIONAL COMPLEXITY TO THE PROBLEM
COMBATING THE SILVER BULLET
DRAWBACKS OF A BRUTE FORCE INCREASE IN THE SYLLABUS
DRAWBACKS OF AN EXTENDED SYLLABUS
INCOMPLETENESS PROBLEMS & AN EXTENDED SYLLABUS
THE HIGH PRIEST AND THE DEITY
AMBIGUITY & AN EXTENDED SYLLABUS
INHERENT AMBIGUITY & AN EXTENDED SYLLABUS
ARITHMETICISATION & AN EXTENDED SYLLABUS
THE LIMITATIONS OF THE HIGH PRIESTS
THE HIGH PRIESTS & AN EXTENDED SYLLABUS
ASSOCIATION LISTS OF QUESTIONS & ANSWERS
THE LIMITATIONS OF KNOWLEDGE & AN EXTENDED SYLLABUS
THE POWER OF ASSOCIATION LISTS FOR ANY SYLLABUS
THERE IS NO COURT OF APPEAL FOR ILL-FORMED QUESTIONS
THE OUTPUT OF COACHING SHOPS
THE LISTS: WHICH SIDE OF THE BREAD IS BUTTERED?
THE PURPOSE OF THE EXAMINATION AS A CAREER OBJECTIVE
THE PURPOSE OF THE EXAMINATION AS A STATUS SYMBOL
THE PURPOSE OF THE EXAMINATION AS A MONEY SPINNER
THE PURPOSE OF THE EXAMINATION AS OPENING AVENUES
THE LIMITATIONS OF SIMULATION & AN EXTENDED SYLLABUS
COACHING SHOPS BECOME SOCIAL INSTITUTIONS
THE WEAKNESS OF INTENSIVE COACHING
ECONOMICS OF THE COACHING INDUSTRY
EPILOGUE


GO TO---->
PREAMBLE
THE WORLD OF MULTIPLE CHOICE EXAMINATIONS
THE WORLD OF VERIFIERS OF SOLUTIONS
THE WORLD OF SOLVERS OF PROBLEMS
THE WORLD OF COMMON SENSE AND COMPUTATION
THE WORLD OF NEGATIVE THOUGHTS AND COMPUTATION



PROLOGUE


(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)

The histrionics of last paragraphs in cracking GATE and rejuvenating the same, are perhaps overdone. With all due regards & respects to the paper setters and examiners of the GATE examination, it is perhaps practically impossible to design a competitive examination question paper which is resistant to the multiple choice silver bullet syndrome.
GO TO---->
PREAMBLE
THE WORLD OF MULTIPLE CHOICE EXAMINATIONS
THE WORLD OF VERIFIERS OF SOLUTIONS
THE WORLD OF SOLVERS OF PROBLEMS
THE WORLD OF COMMON SENSE AND COMPUTATION
THE WORLD OF NEGATIVE THOUGHTS AND COMPUTATION



THE SCOPE OF THE PROBLEM


Consider the multiple choice based tests, assignments, examinations etc. the world over, in all countries, in education, research, government, military, industry and perhaps all spheres of life, throughout one's existence. It is perhaps an annual US$1 trillion human activity. Nobody who is exposed to some semblance of literacy or education in any part of the world can escape them for an entire lifetime.
GO TO---->
PREAMBLE
THE WORLD OF MULTIPLE CHOICE EXAMINATIONS
THE WORLD OF VERIFIERS OF SOLUTIONS
THE WORLD OF SOLVERS OF PROBLEMS
THE WORLD OF COMMON SENSE AND COMPUTATION
THE WORLD OF NEGATIVE THOUGHTS AND COMPUTATION



THE EXTENDED SCOPE OF THE PROBLEM


Even illiterates are subjected at times to a multiple choice based interview/examination for a job.
Before they learn to speak, children are trained/coached in question/answer attacking evaluations based on the multiple choice pattern.
GO TO---->
PREAMBLE
THE WORLD OF MULTIPLE CHOICE EXAMINATIONS
THE WORLD OF VERIFIERS OF SOLUTIONS
THE WORLD OF SOLVERS OF PROBLEMS
THE WORLD OF COMMON SENSE AND COMPUTATION
THE WORLD OF NEGATIVE THOUGHTS AND COMPUTATION



THE FURTHER EXTENDED SCOPE OF THE PROBLEM


We sometimes subject our pedigree pets to a multiple choice test. Perhaps it is an activity of Nature itself.
GO TO---->
PREAMBLE
THE WORLD OF MULTIPLE CHOICE EXAMINATIONS
THE WORLD OF VERIFIERS OF SOLUTIONS
THE WORLD OF SOLVERS OF PROBLEMS
THE WORLD OF COMMON SENSE AND COMPUTATION
THE WORLD OF NEGATIVE THOUGHTS AND COMPUTATION



THE MODEL


To get a good model to study its strong and weak points we can employ the Theory of Computation in a procrustean sense.
GO TO---->
PREAMBLE
THE WORLD OF MULTIPLE CHOICE EXAMINATIONS
THE WORLD OF VERIFIERS OF SOLUTIONS
THE WORLD OF SOLVERS OF PROBLEMS
THE WORLD OF COMMON SENSE AND COMPUTATION
THE WORLD OF NEGATIVE THOUGHTS AND COMPUTATION



THE CONCLUSION ATTEMPTED


The Theory of Computation can be applied to itself to show that a rugged GATE type question paper cannot be designed for the Theory of Computation area, and thus by extension to any other area.
GO TO---->
PREAMBLE
THE WORLD OF MULTIPLE CHOICE EXAMINATIONS
THE WORLD OF VERIFIERS OF SOLUTIONS
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THE RESTRICTIONS USED


The time and syllabus constraints applicable to the GATE examination and similar competitive examinations are used.
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THE STRATEGY


The results and concepts of the venerable area of Computational Complexity when used as a model in a procrustean sense indicate the weakness of the multiple choice pattern.
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ARGUMENT I


A result is that if we want the information content of a choice to be incompressible then the choice is undecidale. This perhaps indicates that all the choices cannot be made equally complex.
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ARGUMENT II


Computational complexity breaks up computations into hierarchies. One can represent a hierarchy and the results associated with components of a hierarchy by an annotated pseudo-Venn diagram.
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THE ANNOTATIONS USED


As in the ancient saying these annotations can be four score and ten in number at a time, per diagram.
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CHARACTERISTICS
OF THE DIAGRAMS-I


These diagrams are basically pictorial in nature, and hence are very user friendly.
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CHARACTERISTICS
OF THE DIAGRAMS-II


As they employ the principle of orthogonally they are excellent visual mnemonic diagrams.
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THE USE OF THE DIAGRAMS


It turns out an instance of this diagram at times allows a large chunk of GATE answers to be obtained by merely glancing or without even looking at the question.
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THE USE OF THE DIAGRAMS ELSEWHERE


Many areas of knowledge have annotated hierarchies which are like the periodic table of Chemistry. In all these areas the same situation arises in the multiple choice pattern.
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THE SCOPE OF THE DIAGRAMS


This sometimes naturally arises whenever anything is 'classified' in any area of knowledge.
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ARGUMENT III


If a choice in a question is complex then it turns out very, very often that the other choices which are in the complement of satisfying set are easy.
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THE EXPLANATION ATTEMPTED


In computational complexity we have parallels with simple finite descriptions becoming exponentially complicated and long finite descriptions. This occurs normally with the use of operators like intersection, complement and a wee bit of nondeterminism.
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ARGUMENT IV


When the intersection of problems which have individually simple solutions is considered one ends up with large complex situations.
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THE JUSTIFICATION ATTEMPTED


The intersection of simple problems makes even the all powerful Turing machine desperate. It has to consult an oracle, its family astrologer.
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THE JUSTIFICATION BY PATTERN MATCHING


The intersection of small length search patterns in Google may result in a search pattern of exponential length.
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THE COMPLEMENT OF A PROBLEM


A problem may be complicated to solve but its complement normally is easily demonstrated or verified.
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COMMON SENSE USE
OF THE COMPLEMENT
ATTEMPTED


If our unpopular noisy neighbor claims he follows all the rules or commandments, and is way ahead of us on the narrow path, it is difficult for us to verify it for every activity he indulges in.
However we can easily and gleefully verify the complement and show that he has done something which violates some rule or commandment or a combination of them, and is merrily going down the broad road.
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THE DIFFICULTY OF FAULT FINDING


However if the problem is to determine a fault, then sometimes it is very difficult, like a famous $1 prize offered for the same. In this case the complement that some, statement or theorem is true is easier to determine.
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ARGUMENT V


Whenever there is some element of choice, guess work or trial and error, like in solving a crossword puzzle or a sudoko game it is called nondeterminism.
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THE EXPRESSIVE POWER
OF
NONDETERMINISM-I


Simple descriptions can arise by employing nondeterminism.
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THE EXPRESSIVE POWER
OF
NONDETERMINISM-II


Removing even a wee bit of nondeterminism results in exponential descriptions. This seems to be unavoidable though difficult to prove that it is always so.
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THE EXPRESSIVE POWER
OF
NONDETERMINISM-III


Sometimes removing nondeterminism guarantees some exponential descriptions in the complement when compared to the original simple descriptions.
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ARGUMENT VI


Computational complexity has identified a large class of problems using simple nondeterministic specifications and naturally occurring in all areas of human activity and knowledge.
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THE EXPRESSIVE POWER
OF
NONDETERMINISM-IV


These have the interesting property that if one can guess a solution to an instance of the problem then it is very easy to verify the correctness of the guess.
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THE EXPRESSIVE POWER
OF
NONDETERMINISM-V


The complement of the problem normally turns out to be very difficult.
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THE EXPRESSIVE POWER

NONDETERMINISM-VI


This results in the existence of a multiple choice question where the correct choice is easy, and the wrong choices which are in the complement difficult.
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ARGUMENT VII


An instance of the problem where the complements to an easy solution are difficult to find is the eternal problem of a person trying to make both ends meet. If a job is there and it is easy to pool up the resources, then the complement is difficult. What happens when the job is lost? How is the balancing to be done?
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A PROBLEM OF INTEREST-I


An instance of the problem where the complements to an easy solution are difficult to find is the eternal problem of a person reaching his destination in a journey. If a bridge is there and it is easy to reach the destination, then the complement is difficult. What happens when the bridge is blown up, or destroyed? How is the target to be reached?
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A PROBLEM OF INTEREST-II


An instance of the problem where the complements to an easy solution are difficult to find is the eternal problem of a person relying on his diary or address book. If the diary or address book is there and it is easy to reach one's social network, then the complement is difficult. What happens when the diary or address book is lost, virus or worm infected, or destroyed? How is the social network to be reached?
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A PROBLEM OF INTEREST-III


An instance of the problem where the complements to an easy solution are difficult to find is the eternal problem of a person packing up his shopping at the checkout counter. If a standard gadget with standard packing is purchased then there is no problem.
If the gadget is bought is bits and pieces then determining the number and size of the carry bags is difficult.
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ARGUMENT VIII


The moral of the story is that the student tackling multiple choice questions should be trained to think parallel (i.e. concurrently).
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THE IMPLEMENTATION OF CONCURRENCY-I


One search for the solution tries to identify the unique simple solution, and the other searches try to isolate the multiple simple choices. Both the searches are to be interleaved.
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THE IMPLEMENTATION OF CONCURRENCY-II


Concurrency can be achieved either by using multiple independent processors or by interleaving sequential processes on a single processor.
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NONDETERMINISTIC THINKING-I


Another moral of the story is that the student tackling multiple choice questions should be trained to think nondeterministically.
This involves guessing the solution and verifying the same.
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NONDETERMINISTIC THINKING-II


Another moral of the story is that the student tackling multiple choice questions should be trained to think nondeterministically.
This involves a brute force method of trying all choices to their logical conclusion.
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THE DEPTH OF SEARCH REQUIRED


Computational Complexity points out that the depth of the search tree can be normally restricted to the size of a succinct description of the problem.
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THE WELL BEHAVED FUNCTIONS


In all branches of knowledge, just as in Computational Complexity, one normally deals only with well behaved functions which are defined almost everywhere.
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THE WEAKNESS
OF WELL BEHAVED FUNCTIONS-I


If we have to choose between multiple different functions we only have to consider the values of the functions for a small number of values in the domain.
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THE WEAKNESS
OF WELL BEHAVED FUNCTIONS-II


This is a very general technique for all quantitative questions in all areas having competitive examinations.
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THE WEAKNESS
OF WELL BEHAVED FUNCTIONS-III


Quantitative questions in so called respectable and revered business school oriented competitive examinations easily fall a prey to this point of view.
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THE WEAKNESS
OF WELL BEHAVED FUNCTIONS-IV


In many cases the context of the question, the area of knowledge being tested, is largely irrelevant.
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THE WEAKNESS
OF WELL BEHAVED FUNCTIONS-V


Questions in Mathematics & Sciences, with syllabus & time restrictions like Talent Search Examinations, easily become howlers in such cases.
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TACKLING HOMOMORPHISM-IARGUMENT IX


A standard trick employed by 'lazy' paper setters of the multiple choice pattern is to attempt to confuse the student by a systematic renaming of symbols. This renaming is called homomorphism in the Theory of Computation.
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TACKLING HOMOMORPHISM-II


Computational Complexity identifies complexity classes which are invariant to the use of homomorphism. It also flags & warns when complexity classes can radically change by the application of homomorphism.
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TACKLING HOMOMORPHISM-III


In traditional areas of knowledge which have centuries of history there is a standardization of the symbols. This is a sacred affair and change is not permitted.
In new areas like The Theory of Computation there is no standardization of the symbols and different standard texts employ different standards. Also in some cases notorious complexity is used like symbols with subscripts, the subscript having subscripts, those subscripts having further subscripts,......
This is very fashionable and leads to undue abstraction.
The student has no choice, he has to answer the questions.
So part of the practice is to get used to this lack of standardization in the symbols, and the standards in the standard texts.
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TACKLING METAMORPHOSES-I


In traditional areas of knowledge which have centuries of history there is a standardization of representations. This is a sacred affair and change is not permitted.
In new areas like The Theory of Computation there is no standardization of the representations of descriptions of computations. Different standard texts employ different standards. Also in some cases notorious complexity is very fashionable and leads to undue abstraction.
The student has no choice, he has to answer the questions.
So part of the practice is to get used to this lack of standardization in the representations of computations, and the standards in the standard texts.
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TACKLING METAMORPHOSES-II


The representation of computing devices or automata is of interest to us. These representations can be pictorial, graphical, tabular of mathematical.
The lack of standardization has led to the student having to encounter a variety of 'multi-headed hydras' of a free for all use of symbols and representations of computations.
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TACKLING METAMORPHOSES-III


The 'pictorial' representation is a machine representation of the automata and not of much interest for our purpose.
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TACKLING METAMORPHOSES-IV


The 'graphical' representations based on annotated, attributed graphs are of great interest for our purpose. A wide variety of variants exist for these representations. The student should practice 'seeing through' the variants in the descriptions. In the case of more powerful machines capable of all 'effective computation' there can be an unbounded number of representations. A very large collection of representations has been catalogued. However, the student is expected to master the representations in the standard texts with variants arising from the use of homomorphism of symbols and slight variations in the description of annotations and attributes of the components of the graph of the representation.
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TACKLING METAMORPHOSES-V


The 'tabular' representations also has some variance, though not as much as the 'graphical' ones. Here also practice is required with the standard variants.
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TACKLING METAMORPHOSES-VI


The 'mathematical' representations as formal mathematical systems are the most notorious. Any amount of undue abstraction and confusion using permutations of the components of the mathematical system, undue and confusing homomorphism of symbols are tools the paper setter can employ. This is done with the excuse that concepts are being tested.
The student requires practice an a mastery of the concepts to attack such unwarranted confusion.
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TACKLING METAMORPHOSES-VII


The 'mathematical' representations as formal mathematical systems are the most notorious.
Continued practice with problems is required to tackle the unwarranted confusion, fear, terror, phobia, neurosis, mania etc. etc. such a gross abuse of 'formal treatments' and 'formal specifications'.
The confusion has a parallel in the network neurosis, PC-phobia, mouse mania, keyboard terror, etc. etc. that the 'human race' felt with the sudden advent of PC and internet based 'ubiquitous computing'.
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TACKLING METAMORPHOSES-VIII


The entire area of Computer Science, Software Engineering and perhaps areas of Information Technology suffer from a lack of standardization.
By an extrapolation the student is required to master variants in the symbols and representations that can be used in all these areas.
Standard examples are the specification of algorithms and detailed specifications through "The Tower of Babel" of Programming languages.
By generalizations the above extends to all new areas of knowledge which are subjected to the multiple choice examination pattern.
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ARGUMENT X


A standard problem any student tackling a multiple choice examination faces is to misread the question. This can result in some symbol, word, phrase or sentence being misunderstood, ignored or imagined to be something else.
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THE MODEL FOR MISREADING A QUESTION


This can be modeled in the Theory of Computation, as the result of the 'birth', 'death', or 'change' of some symbol(s). The last one is some sort of an Ovidian Metamorphoses of the symbol(s).
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FORMAL MODEL FOR MISREADING A QUESTION


Formally, misreading a question is the application of the operation of partial nondeterministic homomorphism or inverse homomorphism.
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THE DANGERS OF MISREADING-I


Computational Complexity warns that this operation can result in a dramatic change in the complexity class.
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THE DANGERS OF MISREADING-II


It can result in enforcing nondeterminism, or lead to partial undecidability or even undecidability.
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THE DANGERS OF MISREADING-III


In the worst case even oracles cannot solve the problem.
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COMMONSENSE
AND
THE EFFECTS OF MISREADING-I


A COMMON SENSE explanation of the effects of misreading is that in any age, culture, civilization or society the 'birth', 'death' or 'turncoat change' of a politician/warlord/spiritual or temporal leader can have dramatic unpredictable results.
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COMMONSENSE
AND
THE EFFECTS OF MISREADING-II


A peaceful/violent economic 'invasion' or 'expulsion' by one section of society by another or 'change' in one section of society can result in serious unintended, unforeseeable consequences.
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TACKLING THE EFFECTS OF MISREADING-I


The moral of the story is that the student attempting a multiple choice examination should practice grasping the essence of the problem carefully.
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TACKLING THE EFFECTS
OF
MISREADING-II


This is different from reading the entire question carefully.
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TACKLING THE EFFECTS
OF
MISREADING-III


The silver bullet demands that the wheat should be separated from the chaff, the essence of the problem should be determined.
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TACKLING THE EFFECTS
OF
MISREADING-IV


At the same time the student should not end up in a fruitless search for a needle in a haystack.
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ARGUMENT XI


A sub area of Computational Complexity is the area of Analysis of Algorithms. This deals with models of problems that arise practically in industrial/practical software or to be specific in the syllabus in question.
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TACKLING ALGORITHMS-I


The 'holy grail' in the Design and Analysis of algorithms in any area is to find an efficient algorithm.
The sad part is that the efficient algorithm normally starts showing its effect asymptotically, for most problems of practical interest.
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TACKLING ALGORITHMS-II


For small values of input an inefficient algorithm is much better than the hi-fi super-duper algorithm which only starts making its effect felt when the input size is sufficiently high.
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TACKLING ALGORITHMS-III


In the multiple choice based examination pattern, the time limitation for each question is very tight.
After all the examiner himself/herself must be able to answer it fast.
So the input values must be small.
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TACKLING ALGORITHMS-IV


The logical conclusion is that a brute force algorithm is best suited for the solution of problems using the multiple choice pattern.
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TACKLING ALGORITHMS-V


The next step is not to use any formal algorithm but a brute force enumeration of inputs and results catering to the various choices in the question.
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TACKLING ALGORITHMS- VI


Experimental evidence indicates the surprising phenomenon that the brute force method is a very generally applicable strategy. It is of great value in all examinations based on the multiple choice pattern, with a syllabus and time constraint.
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TACKLING ALGORITHMS-VII


The brute force method effectively says that the less one knows of the subject and more of COMMON SENSE the student employs the better off he/she is.
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TACKLING ALGORITHMS-VIII


The COMMON SENSE explanation is easy. If one has to walk up to the gate of one's house/college/place of work and one is in a hurry the fastest method is to walk. There is no point waiting for a bus/car/train/plane/rocket to turn up.
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TACKLING ALGORITHMS-IX


The expensive fast modes of transport have a starting time. A plane takes hours at time to take off, the rocket days on end.
The pedestrian who walks is best off for small distances.
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TACKLING ALGORITHMS-X


The pedestrian is best of most of the time in multiple choice based, time and syllabus limited examinations.
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TACKLING ALGORITHMS-XI


In real life one can walk across and formally claim in front of our normal fussy aunt that we have come in a luxury car.
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TACKLING ALGORITHMS-XII


The student can formally claim to have used some hi-fi super-duper algorithm but actually and practically used a brute force method.
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TACKLING ALGORITHMS-XIII


Computational Complexity has a formal explanation for all this. The complexity classes form a hierarchy, like a pseudo-Venn diagram.
For small input sizes the complexity class degenerates to trivial complexity classes, enabling simple algorithms or the brute force method.
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TACKLING ALGORITHMS-XIV


Computational Complexity however cautions the student to be careful. Normally functions are only defined almost everywhere. This means for some finite number of values they are not defined. So one should be careful when small values are used, to see that they are within the scope of the problem.
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TACKLING ALGORITHMS-XV


Computational Complexity deals with well behaved functions. Any animal or human being is born some time and is an infant and passes through childhood. As a child a sumo wrestler can be tackled by practically anybody. A lion club can be bullied by us. The problem is when they grow up.
Similarly the function at the origin and for small values in the domain has a gestation period, when it can be easily tackled. This is so even if the function is a monster like an exponential, double exponential or even a notorious Ackermann's function.
So when we use the rule for functions to 'catch them young', then we find a lot of choices can normally be eliminated in the multiple choice question.
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TACKLING ALGORITHMS-XVI


[ COMMENT to self:- a point of mathematical philosophy.]
Computational Complexity deals with well behaved functions. Any animal or human being gets old sometime. As a geriatric a sumo wrestler can be tackled by practically anybody. An aged lion can be kicked around by a donkey. The problem is there in actual nature.
However, since we deal only with asymptotic functions which we call well-behaved, we restrict the class of recursive functions in computer science and mathematics. We do not allow old age for functions. We demand the principle of mathematical induction apply. There is no question of any camel's back being broken as the 'number' of straws on its back increases.
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WELL FORMED QUESTIONS


A well formed question in an examination based on the multiple choice pattern is one where one of the answers can be assumed to be correct and the rest are wrong.
If the paper setter has taken care then it can be assumed that every question is a well formed question.
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ILL FORMED QUESTIONS


An ill formed question in an examination based on the multiple choice pattern is one where zero or more of the answers can be assumed to be correct and the rest are wrong.
If the paper setter has taken not taken care then it can be assumed that such 'howlers' may arise.
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STANDARD EXAMINATIONS


A standard competitive examination is one where the questions can be assumed to be only well formed questions.
Ill formed questions in an examination based on the multiple choice pattern are to be abandoned by the student based on a 'time out' based approach.
Such 'howlers' may arise in any of the standard examinations also.
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NON-STANDARD EXAMINATIONS


A non-standard competitive examination is one where the questions can be assumed to be probably ill formed questions.
The situation for the student is much harder in this case.
Ill formed questions in an examination based on the multiple choice pattern are to be abandoned by the student based on a 'time out' based approach.
Such 'howlers' may arise in any of the non-standard examinations, tests, and guides of average to dubious repute.
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>
STANDARD EXAMINATIONS ASSUMED


A standard competitive examination is one where the questions can be assumed to be only well formed questions.
This is what we consider for our study and model.
We will assume a mature competitive examination where great care is taken to see that no ill formed questions are present.
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FOLK THEOREM BASED ON EXPERIENCE


For any problem to be tackled, if one knows for certain that a solution is possible then it is easy to find the solution.
If however one does not know if a solution to a problem exists or not then it is very difficult to find the problem.
It may happen that a solution to the problem may not exist.
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JUSTIFICATION OF THE FOLK THEOREM-I


If a solution is granted to exist for a problem, then a nondeterministic succinct formulation of the problem is normally possible.
The depth of the solution using nondeterminism as shown by Computational Complexity is normally small in relation to the size of the problem.
If the solution is not known to exist then we may end up with deep search trees, partial decidability or even undecidability.
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JUSTIFICATION OF THE FOLK THEOREM-II


In a standard competitive examination only well formed questions are present. So a succinct nondeteministic formulation of the problem for the correct and false choices can be taken.
The nondeterministic behavior can be extended to include alternation for the correct choice and the wrong choices. Computational Complexity indicates that a small effort is normally sufficient to resolve the question.
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THE CONSULTANT


In real life when one has a problem one goes to a consultant. This could be a financial consultant, a family doctor, a society leader, an elder in the family.
Such a person will study our mixed up problems, and the knots we have got ourselves into and put order into the situation so that we can tackle it.
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THE CONSULTANT IN COMPUTATIONAL COMPLEXITY


In the area of Theory of Computation and Computational Complexity we have what are called 'regular' complexity classes. A complexity class does not lose its status as a result of intersection with a member of the 'regular' class. It remains in the same class.
The advantage is that just like the consultant order is put into mixed up behavior and it is easy to spot the difficulties and properties hence answer the question easily.
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THE REGULAR CLASSES IN COMPUTATIONAL COMPLEXITY


In Computational Complexity we have what are called 'regular' complexity classes. These are like a template or mould into which we can force the input to the problem, or statement of the problem . This occurs in many areas of knowledge.
As a complexity class is invariant as a result of intersection with a member of the 'regular' class.
The advantage is that just like the financial consultant, social consultant, etc. in real life, order is put into mixed up behavior and it is easy to spot the solution to the question easily.
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THE PROOF FINDING METHODS-I


In cultures oriented heavily to 'proof finding' in mathematics there are some accepted proof techniques.
These techniques can be used to determine the easy 'wrong answers' in the multiple choice question.
One of them is the pigeon hole principle. If we have a bunch of pigeon holes and less pigeon holes than pigeons and we have been able to place all the birds in the holes, then some pigeon hole contains more than one pigeon.
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THE PROOF FINDING METHODS-II


In Computational Complexity we use at times a sliding window on the input.
We require that for all positions of the window some property must be satisfied. Sometimes we demand that for at least one position of the window some property must be satisfied.
At times we have multiple windows related to each other and slide them on the input.
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PUMPING ON WHAT WE SEE IN THE WINDOW


The above technique allows us to 'pump' on something we see through the window at some position or all positions depending on our requirement.
This is used at times to show that some element is not a member of some complexity class.
This method is an application of the pigeon hole principle.
This technique can be used to find the easy 'wrong answers'.
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THE PROOF FINDING METHODS-III


A standard proof technique is the use of mathematical induction.
This can be used to determine the 'wrong answers' to the question much more easily than the right answer at times.
This is especially valid when we have to choose the correct function from a choice of four functions.
Depending on the situation mathematical induction directly finds the easy right answer or eliminates the easy wrong answers.
It is assumed we use nondeterminism with alternation to choose between the two paths.
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THE PROOF FINDING METHODS-IV


A standard proof technique is the use of proof by contradiction.
One can start off for each choice in the question that it is the answer. Then we proceed to show that this leads to a contradiction at times. Such choices can be eliminated.
We assume we are going to use nondeterminism with alternation. The search tree is restricted in depth. The input is of exponential size compared to it. This as in the standard examination one question is definitely correct and the others wrong. We end up with an easy method to find the solution.
To implement the nondeterminism we try the choices concurrently in a brute force manner. Alternatively, we modify the effort by guessing the solution and checking the results of our guess. Experience with solving a lot of questions helps in this guessing game.
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THE PROOF FINDING METHODS-V


A standard proof technique is to eliminate some of the choices by showing that they are only part of the required result but not the whole result.
In formal terms we show that the set represented by the choice is a proper subset of the set representing the solution, and the other way around does not work.
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THE PART AND THE WHOLE


One can start off for each choice in the question that it is the answer. Then we proceed to show that this leads to a contradiction at times, by showing that the 'part cannot be the whole'. Such choices can be eliminated.
We assume we are going to use nondeterminism with alternation, and restriction of the depth of the search tree as before. To implement the nondeterminism we try to guess the result and verify it, or go the whole hog and use a brute force method.
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THE PROOF FINDING METHODS-VI


Other proof techniques either standard or modified but acceptable can be used, just as in the case of solving problems by other methods.
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THE PROOF FINDING METHODS-VII


The major difference is that we are concentrating on the wrong choices and the wrong answers. These are simpler than solving the full question.
So we are becoming experts in determining all the wrong answers, and know everything that is not in the subject.
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THE PROOF FINDING METHODS-VIII


Throughout our attempts to find the solution we use concurrency and alternation with nondeterminism in our methods. We implement nondeterminism in all its variants, either demanding the longest path, the shortest path, all paths, and the longest path with the ability to backtrack efficiently, ability to guess the certificate of proof and verify it and so on.
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THE PROOF FINDING METHODS-IX


In general the student can risk using probability. The choices can be excluded based on a 'high probability' of being correct/incorrect.
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THE PROOF FINDING METHODS-X


The student becomes an Interactive Verifier. He needs a reliable Solver for interactive Verification.
The 'guarantees' by the paper setters of 'reliable' and 'standard' multiple choice based examinations provides this.
In the multiple choices one choice is definitely correct so it doubles up as a Solver.
In the multiple choices the rest of the choices are definitely wrong so these double up as Solvers.
The student has to practice use concurrency, nondeterminism and alternation to guess the Solver.
The syllabus, time constraints, the power of the intersection & complement operations guarantee a small depth of the search tree.
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THE PROOF FINDING METHODS-XI


The preceding discussions can be formalized using Computational Complexity. We have the situation of Interactive Verifiers and reliable Solvers of problems.
By a small procrustean application the famous theorem in Computational Complexity that IP=PSPACE as very much valid to serve as a model.
According to the theorem the knowledge areas and problems are modeled as being in PSPACE as an upper bound which in reality is adequate. This can span all MULTIPLE CHOICE EXAMINATIONS of interest.
The theorem models an average to above average Verifier as compared to a very 'clever' Solver i.e. the paper setter.
In reality subsets of PSPACE and subets of P are adequate. PSPACE is as per Computational Complexity a "well behaved" large complexity class closed under nondeterminism, complement, etc. etc., and including all of NP.
Application of the theorem shows the paradox that more the effort the paper setters put in to obtain reliable, correct questions the easier it is for the "Interactive Verifier" as he has easy access to reliable 'solutions'. These solutions are the easy right choice and difficult wrong choices or vice versa.
Throughout our attempts to find the solution we use concurrency and alternation with nondeterminism in our methods. We implement nondeterminism in all its variants, either demanding the longest path, the shortest path, all paths, and the longest path with the ability to backtrack efficiently, ability to guess the certificate of proof and verify it and so on.
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TWO GENERAL TECHNIQUES

Two general techniques that can be used with many quantitative questions to make them simple are considered.
We will call them 'deformalisation' &'instantiation'.
Both depend on the general strategy of 'verbalisation' of the problem as the first step.
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VERBALISATION

A general strategy to cut down the fear caused by excessive formalization is to 'verbalise' the problem.
It does not matter which natural language is employed for this purpose. It has been found again and again that 'verbalising' the problem, leads to the problem becoming user friendly and easier to solve.
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GENERALISATION

A general strategy to cut down the fear caused by excessive formalization is to realize that 'generalisation' normally leads to dilution of the complexity. This is the phenomenon in mathematics that it is easier to solve the general problem. The profound eternal problem is the determination of the right generalisation.
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EXPLOITING GENERALISATION

Sometimes 'generalisation' forces the quantitative treatment of the problem to work for very small values. This allows the student to find out the false answers by considering the values of the quantitative formulations for small values in the domain.
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DEFORMALISATION

Depending on the problem one can deformalise the problem to allow only part of the domain as input values. This will at times aid in filtering out the wrong choices.
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INSTANTIATION

A general strategy to cut down the fear caused by excessive formalization is to 'VERBALISE' the problem, subject it to 'DEFORMALISATION' and then 'INSTANTIATE' the problem for a suitable real life situation.
Many GATE problems can be solved by using COMMON SENSE with this strategy.
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REFORMALISATION

The next step is to 'REFORMALISE' the inferences and deductions from the 'INSTANTIATION'. The reformalisation should be in terminology and use the formalism of the knowledge area of the question.
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DEMONSTRATION-I

A general strategy using 'VERBALISATION', 'DEFORMALISATION' and 'INSTANTIATIATION' is now considered.
In GATE questions dealing with scheduling concurrent computations one can consider the concepts of concurrency taking real life examples from the environment.
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CONCEPTS IN CONCURRENT COMPUTATION

Just consider a person and his three neighbors having an appointment with a doctor at almost the same time.
Appointment or no appointment, we have all the concepts of concurrent programming, in a real situation.
With our noisy neighbor around we have both 'busy wait' and 'starvation'. We can simulate the effects of 'monitors', 'semaphores', 'synchronisation', 'message passing', 'deadlocks', etc. etc. in the environment.
All scheduling algorithms in the syllabus can be simulated.
Most GATE questions in concurrency & scheduling can be modeled and easily be solved by commonsense reasoning using the above model.
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DEMONSTRATION-II

Another general strategy using 'VERBALISATION', 'DEFORMALISATION' and 'INSTANTIATIATION' is now considered.
Most questions dealing with partial undecidability and Turing machine, or r.e set or recursive set based can be reduced to simple commonsense reasoning.
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THE UNDECIDABLE

Another general strategy using 'VERBALISATION', 'DEFORMALISATION' and 'INSTANTIATIATION' is now considered.
We just have to ask a couple of our noisy self-proclaimed generous neighbors for a small hand loan.
The results teach us in a very user-friendly way, the meaning of the concepts of decidability, undecidability, partial decidability, algorithms, procedures, r.e. sets, recursive sets, Turing decidability etc. etc.
Most questions dealing with partial undecidability and Turing machine, or r.e set or recursive set based can be reduced to simple commonsense reasoning.



THE DECIDABILITY
OF
PARTIALLY DECIDABLE SETS

Another general strategy using 'VERBALISATION', 'DEFORMALISATION' and 'INSTANTIATIATION' is now considered.
We just have to ask a couple of noisy self-proclaimed benevolent neighbors about the activities of the terrible 'urchin' in the neighborhood. We get all, and only the bad reports.
If we ask the urchin's devoted mother about the urchin we get only the good reports about the apple of her eye.
Listening to both sides gives us the full picture.

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THE DECIDABILITY
OF
PARTIALLY DECIDABLE SETS(contd)

Another general strategy using 'VERBALISATION', 'DEFORMALISATION' and 'INSTANTIATIATION' is now considered.
By listening not only to the persons in power and also to what the opposition has to say, gives us the full picture.
We get the intersection of two enumerations. One gives all the 'good' things, the other gives all the 'bad' things. The net result is that we know all the characteristics.
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DEMONSTRATION-III

The general strategy using 'VERBALISATION', 'DEFORMALISATION' and 'INSTANTIATIATION' can be applied to other areas of Computer Science. The preceding states the famous result that if a set and its complement are both r.e. then the set is recursive.
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DEMONSTRATION-IV

Still another general strategy using 'VERBALISATION', 'DEFORMALISATION' and 'INSTANTIATIATION' is now considered.
Most questions dealing with concepts relating to intractability, NP-completeness etc. and restricted to the syllabus can be reduced to simple commonsense reasoning.
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NP-COMPLETENESS

Still another general strategy using 'VERBALISATION', 'DEFORMALISATION' and 'INSTANTIATIATION' is now considered.
NP-complete and NP-hard problems can be likened to exclusive clubs, where membership is by invitation.
The invitation must be from a bona-fide member of the club.
This is sufficient for a problem to be NP-hard. To be NP-complete one must show that the problem is a citizen of the country in question.
Computational Complexity has identified many domains where they are '-complete' problems.
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NP-COMPLETENESS
DEMYSTIFIED - I

Still another general strategy using 'VERBALISATION', 'DEFORMALISATION' and 'INSTANTIATIATION' is now considered.
Computational Complexity has identified many domains where they are '-complete' problems.
One strategy that can be followed to convert some other country, social group etc. to our way of life, our way of thinking, our control, our domination, our ethics, our mores, our culture, our value system etc. etc. is to get hold of some 'kingpin goon', 'Quisling', etc, in the other country or society. If that person can be converted then the whole, country is converted to our viewpoints and direction.
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NP-COMPLETENESS
DEMYSTIFIED - II

Still another general strategy using 'VERBALISATION', 'DEFORMALISATION' and 'INSTANTIATIATION' is now considered.
Computational Complexity has identified many domains where they are '-complete' problems.
These are the 'king pin goons'.
The police regularly use the strategy to break up gangs of goons.
The teacher regular tries to catch 'the bad egg' in the class.
A lot of people, societies, institutions, governments try to find the 'Quislings' in some other bunch of people, societies, institutions, governments, countries and so on.
The strategy has been adopted from time immemorial countless number of times by one religion to swallow up another.
The strategy has been adopted for one country to swallow up another.
We always want to know 'the people who matter'
We always try to find a 'scapegoat'.
We or traditional brands of History are only interested only in the 'people who matter'.
We want to report to the "CEO" only, he is the only person who matters.
We want to destroy the 'eye' of the cyclone.
It is commonly used to tackle political, social and industrial unrest, the world over.
If we can find and influence the 'Big Chief', 'the leader', 'the High Priest', 'the King', 'the Emperor', etc. it is sufficient for everyone to fall in line.
The idea is to 'make an example of' or 'get full control' with minimum effort.
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NP-COMPLETENESS
DEMYSTIFIED - III

Still another general strategy using 'VERBALISATION', 'DEFORMALISATION' and 'INSTANTIATIATION' is now considered.
How does a '-complete' club get started? There are many complexity classes with these 'kingpin goons' or 'Quislings'.
They are not guaranteed to exist for all classes. Just as a 'Quisling' cannot always be found in all societies, countries, all activities.
Somebody must first find an initial 'Adam' to get the club going. Then we can have a 'nucleus' of members. Then the club can expand and explode in membership.
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NP-COMPLETENESS
DEMYSTIFIED - IV

Still another general strategy using 'VERBALISATION', 'DEFORMALISATION' and 'INSTANTIATIATION' is now considered.
How does a '-complete' club get started? The fun started about half a century ago. The eminent Prof. Stephen Cook considered the complexity class NP. For this class he found a 'kingpin goon' called the satisfiability problem. This one is the 'Adam' of the club of NP-complete problems.
Now this problem could extend invitations to other problems to join the exclusive club.
There should be a Verification that the 'goon' invited to the status of a 'king pin goon' is a bonafide member of NP.
There is no 'application' for membership allowed.
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NP-COMPLETENESS
DEMYSTIFIED - V

Still another general strategy using 'VERBALISATION', 'DEFORMALISATION' and 'INSTANTIATIATION' is now considered.
How does a '-complete' club grow? The eminent Prof. Karp used the 'Adam', the satisfiability problem, for extension to a small nucleus of important problems that had led mathematicians over centuries to lifetimes of tears, toil, sweat and despair. He thus showed that this small nucleus of problems were 'king pin' goons and there seems to be a relation between the concept of '-complete' and the incorrigible nature of these problems which resisted centuries of attack.
Then for about a decade people had a 'ball' isolating the 'king pin' goons and as on today 4000 of them are known, to be bonafide 'king pin goons' of the NP complexity class.
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DEMONSTRATION-V

The general strategy using 'VERBALISATION', 'DEFORMALISATION' and 'INSTANTIATIATION' can be applied to most areas of knowledge where underlying concepts of a general scientific nature are subjected to a quantitative treatment.
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DEMONSTRATION-VI

The general strategy using 'VERBALISATION', 'DEFORMALISATION' and 'INSTANTIATIATION' can be explained by Computational Complexity.
In the hierarchy of Complexity Classes, any particular class includes all the classes below it. We are merely considering smaller, special and perhaps elementary members of a particular Complexity Class.
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APPLICATION OF COMPUTATIONAL COMPLEXITY


Other results of Computational complexity can be used as strategies that can be employed by Verifiers to obtain the answer without actually Solving the problem.
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COMBATING THE SILVER BULLET


One solution to combat use of the silver bullet which suggests itself is to vastly increase the syllabus and thus the information content of the question.
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DRAWBACKS OF EXTENDING THE SYLLABUS


[Topics to be elaborated upon========>>
1. [Ambiguity] In the multiple choice based examination pattern, the paper setter may employ psedo-ambiguity in an attempt to create difficult questions. This results in two choices being possible answers. Careful interpretation of a 'word' or 'phrase' allows the right choice to be made.
2. [Pseud-ambiguity] An example is the ubiquitous quantitative multiple choice question of determining the next element of a given sequence of numbers. Ostensibly they form a series. If one takes supersets of the syllabus an unbounded number of solutions exist. One can trace umpteen curves through al those numbers in the Euclidean plane. However the student must restrict himself to the syllabus.
3. [Inherent Ambiguity] The paper setter sometimes oversteps himself and creates a ‘howler’ where all the choices are correct/wrong. There is normally no ‘effective’ Court of Appeal.
4. [Supersets of the syllabus] If one extends the syllabus then wrong answers may become correct or the other way around. Computational Complexity based arguments show that extensions to the syllabus effectively increase the complexity class modeling the syllabus. A simple syllabus can use a simple complexity class.
5. [Arithmeticization] Any area of knowledge can be reduced to simulations based on Arithmetic. So by extension all areas of knowledge are only worried about the true statements of Arithmetic.
6. [Type 1 Incompleteness] If one extends the syllabus sufficiently then the first type of Incompleteness sets in. The student will not know when to ‘stop’/’halt’ in his search for the validity of a choice in some question.
7. [Type 2 Incompleteness] With a sufficiently large superset of the syllabus a second type of Incompleteness sets in. The student will never be able determine the ‘reasons’ by which a particular choice in some question is right/wrong.
8. [Type 3 Incompleteness] An oracle may help the student tackle some types of Incompleteness, but there are problems for which an oracle will not help. The student cannot determine in a finite amount of time the validity of a choice.
9. [Type 4 Incompleteness] An hierarchy of oracles may help the student in some cases, but there are problems beyond any finite hierarchy of oracles.
10. [Type 5 Incompleteness] There are problems the student cannot attack with the use of oracles.
11. [Type 6 Incompleteness] There are problems in the real world for which the simulations blow up. They become larger and larger for smaller and smaller problems. Ultimately the student knows ‘everything’ about ‘nothing’.
12. [Tackling Incompleteness] If the student is educated/trained/coached to refer to an association list of (question,answer) pairs, then the student just looks up answers in this list.
13. [The High Priest] In the temple of any religion the High Priest(s) and minions are more important then the Deity. The clerk is more important than the officer in any government organization.
14. [The Teacher as the High Priest] In any educational/instructional setup the Teacher is more important than the Knowledge. The business of the student is to satisfy the examiner in a multiple choice examination.
15. [The Syllabus as the High Priest] The association list of question, answer pairs based on the prescribed syllabus is what matters. The validity of the same cannot normally be posed as a question/discussion to a faceless, nameless, invisible entity called the examiner.
16. [Knowledge and the High Priest] At any point of time, in any area of knowledge, the association lists of acceptable/correct [question, answer] pairs are determined and fixed in an area. This is decided by the leaders & is normally valid for a generation. In some cases the validity may exist for a couple of generations. When longer periods are involved it gets pushed into a 'high school' syllabus.
17. [The Duty of the Student] It is the duty of the student to satisfy the examiner & choose the answer the examiner wants.
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DRAWBACKS OF A BRUTE FORCE INCREASE
IN THE SYLLABUS


There is however a basic limitation and a backlash. The syllabus cannot be increased beyond the limits of the proposed course.
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TACKLING AN EXTENDED SYLLABUS


If the student studies 2-3 years ahead well into his proposed course of study, the silver bullet grows enormously in size for questions relating to the basic syllabus.
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THE OUTPUT OF COACHING SHOPS


The student becomes a Verifier of solutions of the proposed course and cannot easily become a Solver of problems in the proposed course.
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THE WEAKNESS OF AN EXTENDED SYLLABUS


The coaching shops have taken care of the increased syllabus also in some cases.
Students are coached over years, from the wee hours of the morning till late night, to master the question answer sets.

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COACHING SHOPS BECOME SOCIAL INSTITUTIONS


Honorary doctorates have been conferred by well meaning educational institutions on persons who specialized in the use of the silver bullet.
However, as Mark Twain may have remarked, few escape that distinction.
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THE WEAKNESS OF INTENSIVE COACHING


Students indoctrinated as Verifiers of solutions make the mark, and they find it difficult to become Solvers of Problems from then on.
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ECONOMICS OF THE INDUSTRY



The national coaching industry is an annual US$5 billion affair, so by extrapolation the multiple choice based evaluation system is perhaps an annual US$1 trillion human activity when we consider the whole world.
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EPILOGUE


Based on experimental evidence, masses of Verifiers of solutions are successfully created.




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CRACKING COMPETITIVE EXAMINATIONS
THE “SILVER BULLET” IN COMPETITIVE EXAMINATIONS
THE GOOD PART OF COACHNG SHOPS
THE WORLD OF MULTIPLE CHOICE EXAMINATIONS
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I. SOLUTIONS TO PREVIOUS GATE THEORY OF COMPUTATION PAPERS.

II. THEORY OF COMPUTATION QUESTION BANK

III. ALGORITHMS FOR GATE

IV. QUESTIONS IN LANGUAGE PROCESSORS FOR GATE

V. FAIRY TALES AND INTRACTABILITY

VI. METAMATHEMATICS FOR PRIMARY SCHOOLS

VII. METAMATHEMATICS FOR DUMMIES
VIII. ALGORITHMS FOR DUMMIES--PPTs

IX. COMPUTER SCIENCE LITERACY IN PRE-AGRARIAN AND TRIBAL SOCIETIES

X. COMPUTER SCIENCE LITERACY IN PRIMITIVE SOCIETIES

XI. DISCUSSION ON ALGORITHMS

XII. INTRACTABILITY FOR PRIMARY SCHOOLS

XIII. THEORY OF COMPUTATION MADE EASY

XIV. THEORY OF COMPUTATION FOR SECONDARY SCHOOLS

XV. PROVEN NOTES & QUESTION BANK IN THETHEORY OF COMPUTATION

XVI. SERIOUS DISCUSSION FORUM

XVII. INTRACTABILITY MADE EASY

XVIII. CRACKING COMPETITIVE EXAMINATIONS

XIX. THE “SILVER BULLET” IN COMPETITIVE EXAMINATIONS

XX. THE GOOD PART OF COACHNG SHOPS

XXI. THE BAD PART OF COACHING SHOPS

XXII. PREAMBLE TO A FORMAL STUDY OF MULTIPLE CHOICE BASED COMPETITIVE EXAMINATIONS

XXIII. THE WORLD OF MULTIPLE CHOICE BASED EXAMINATIONS

XXIV. THE WORLD OF VERIFIERS OF SOLUTIONS

XXV. THE WORLD OF SOLVERS OF PROBLEMS

XXVI. THE WORLD OF COMMON SENSE AND COMPUTATION

XXVII. THE WORLD OF NEGATIVE THOUGHTS AND COMPUTATION

XXVIII. INTRACTABILITY AND COMMON SENSE

XXIX. COMPUTER SCIENCE LITERACY IN FEUDAL SOCIETIES

XXX. COMPUTER SCIENCE LITERACY IN RURAL SOCIETIES WITH TRACES OF THE INDUSTRIAL REVOLUTION










START OF STRAY THOUGHTS


[I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS! [I NTERACTIVE] VE RIFIERS!




PART II
THE WORLD OF VERIFIERS OF SOLUTIONS





CONTEN TS

(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)

PROLOGUE--THE PROBLEM
THE BIGGER PICTURE OF THE ENVIRONMENT
THE PURPOSE OF THE EDUCATIONAL PROCESS IN THE ENVIRONMENT
THE ENVIRONMENT I: AS PER THE MEDIA REPORTS
OBSERVATION I: THE CONCEPT OF IMPORT SUBSTITUTION
OBSERVATION II: MEGAPROJECTS AND THEIR IMPLEMENTATION
OBSERVATION III: VERIFIERS OF SOLUTIONS OF LABOUR
OBSERVATION IV: THE REUSE OF SOLUTIONS
OBSERVATION V: THE JOB AND STATUS OF THE SOLVER OF PROBLEMS
THE ENVIRONMENT II: THE PHILOSOPHY OF MACAULAY
OBSERVATION VI: VERIFIERS OF SOLUTIONS AND PROCEDURES
THE ENVIRONMENT III: THE EDUCATIONAL PROCESS IN THE ENVIRONMENT
OBSERVATION VII: THE PLIGHT OF TEACHERS IN THE ENVIRONMENT
OBSERVATION VIII: THE EFFECTS OF AN INCREASED SALARY
OBSERVATION IX: THE PHOBIAS OF THE OLD TEACHERS
OBSERVATION X: THE KEYBOARD SYNDROME
OBSERVATION XI: THE MECHANICAL TYPEWRITER IS STILL AROUND
OBSERVATION XII: THE VERIFIERS OF SOLUTIONS
OBSERVATION XIII: TACKLING NEW AREAS OF KNOWLEDGE
OBSERVATION XIV: THE MATERIAL FOR KNOWLEDGE
OBSERVATION XV: ONLY VERIFIERS OF SOLUTION ARE PRODUCED
THE ENVIRONMENT IV: THE ROLES OF SOLVERS AND VERIFIERS IN COACHING
THE ENVIRONMENT V: THE RELATIONSHIP BETWEEN CHAOS AND STARS
OBSERVATION XVI: THE COLLECTIVE WISDOM OF THE STUDENT COMMUNITY
OBSERVATION XVII:WHAT IS IN A NAME? OBSERVATION XVIII: THE CREATION OF BULLET PROOF DOCUMENTATION
OBSERVATION XIX: THE STUDENTS EVOLVE A SOLUTION
THE CREATIVE SOLUTION OF THE STUDENTS
THE NET RESULT: VERIFIERS OF SOLUTIONS ARE TURNED OUT
THE IP=PSPACE MODEL
PROCRUSTEAN USE OF THE MODEL
INFERENCES I: MASTERY OF KNOWLEDGE
INFERENCES II: THE KNOWLEDGE IN PSPACE
INFERENCES III: THE POWER OF PSAPCE
INFERENCES IV: ASSESSING THE KNOWLEDGE ACQUIRED
INFERENCES V: THE PROPERTIES OF PSPACE
INFERENCES VI: ACQUIRING NONDETERMINISTIC THINKING
INFERENCES VII: ACQUIRING SKILLS IN GUESSING SOLUTIONS
INFERENCES VIII: ONLY VERIFIERS OF SOLUTIONS ARE TURNED OUT
A PHENOMENON EXPLAINED
INFERENCES IX: THE USE OF THE INVISIBLE COLLEGES
INFERENCES X: THE RELIABILITY OF THE SOLVER IN THE MODEL
INFERENCES XI: THE 3-TIER MODEL
INFERENCES XII: RECURSION AND MUTUAL RECURSION IN THE LEARNING PROCESS
INFERENCES XIII: THE AVAILABILITY AND USE OF INSTRUCTORS
INFERENCES XIV: THE PERFECT SOLVER IN THE MODEL
INFERENCES XV: THE EFFECTS OF DEGENERATION IN THE SOLVER IN THE MODEL
INFERENCES XVI: THE EFFECT OF A POOR SOLVER
INFERENCES XVII: PUSHING A VERIFIER OF SOLUTIONS TO BECOME A SOLVER
INFERENCES XVIII: THE SOLVER VANISHES IN THE MODEL
INFERENCES XIX: THE SITUATION OF THE STUDENT
INFERENCES XX: OUT OF CHAOS STARS ARE BORN
ANOTHER PHENOMENON EXPLAINED
ANOTHER PHENOMENON EXPLAINED FURHTER
EXTENSIONS TO THE MODEL
INFERENCES XXI: A VERIFIER TRIES TO BECOME A SOLVER
INFERENCES XXII: THE DIFFICULTIES OF A VERIFIER TO BECOME A SOLVER
INFERENCES XXIII: THE PHOENIX AND STARS
OBSERVATION FROM THE HISTORY OF SOFTWARE ENGINEERING
INFERENCES XXIV: A SILVER BULLET FOR SOFTWARE DOES NOT EXIST
INFERENCES XXV: THE IQ OF THE VERIFIER OF SOLUTIONS MUST BE VERY HIGH
INFERENCES XXVI: THE NEED FOR EXCELLENT VERIFIERS OF SOLUTIONS
A SITUATION EXPLAINED
A SITUATION FURTHER EXPLAINED
INFERENCES XXVII: THE OPPORTUNITIES FOR HIGH IQ VERIFIERS
INFERENCES XXVIII: THE RELATIVE DEMANDS FOR SOLVERS AND VERIFIERS
INFERENCES XXIX: HEADHUNTERS AND VERIFIERS
INFERENCES XXX: A BILLION VERIFIERS OF SOLUTIONS WANTED
INFERENCES XXXI: THE ECONOMICS OF CHEAP VERIFIERS OF SOLUTIONS
INFERENCES XXXIII: THE REQUIREMENTS OF VERIFIERS IN THE GLOBAL VILLAGE
INFERENCES XXXIV: THE GLOBAL VILLAGE NEEDS EDUCATED VERIFIERS OF SOLUTIONS
THE ENVIRONMENT REVISITED I: THE BULK OF THE PEOPLE IN THE ENVIRONMENT
OBSERVATION I: THE BANKRUPTCIES
OBSERVATION II: THE CYCLONES
OBSERVATION III:'THE ETERNAL QUEST'
THE ENVIRONMENT REVISITED II: 'SOMEBODY MUST DO SOMETHING'
OBSERVATION IV: THE STUPIDITY OF REINVENTING THE WHEEL
OBSERVATION V: EVERYONE WANTS TO BE A VERIFIER OF SOLUTIONS
OBSERVATION VI: THE CULTURE OF SOLVERS AND VERIFIERS
THE ENVIRONMENT REVISITED III: THE TV SHOWS OF THE VERIFIERS
OBSERVATION VII: THE ARISTOCRATS OF THE WORLD
OBSERVATION VIII: HOW A VERIFIER OF SOLUTIONS BEHAVES IN ROME
THE ENVIRONMENT REVISITED IV: VERIFIERS ONLY REUSE SOLUTIONS
OBSERVATION IX: THE 'CUT AND PASTE' CULTURE
OBSERVATION X: THE MULTIVALUED LOGIC ENVIRONMENT
OBSERVATION XI: THE LOWLY STATUS OF SOLVERS OF PROBLEMS
OBSERVATION XII: THE DIGNITY OF PLAIGARISM
OBSERVATION XIII: REUSE AND THE INTERNET
OBSERVATION XIV: THE CONTINENT OF CIRCE
OBSERVATION XV: DR JEKYL AND MR HYDE
OBSERVATION XVI: THE RESEARCH OF THE VERIFIERS OF SOLUTIONS
OBSERVATION XVII: THE RIGID ADHERENCE TO DOCUMENTATION OF PROCEDURES
THE ENVIRONMENT RECONSIDERED: ORIGINALITY IS A JOKE
OBSERVATION XVIII: THE FEUDAL ARISTOCRATIC MINDSET
OBSERVATION XIX: PRE-AGRARIAN AREAS IN THE ENVIRONMENT
OBSERVATION XX: THE DIVINE RIGHT OF THE ARISTOCRAT
OBSERVATION XXI: THE MINION SHOULD KNOW HIS PLACE
OBSERVATION XXII: THE ARISTOCRATIC WARS OVER CREDIT TAKING
OBSERVATION XXIII: OVERDONE PLAIGARISM
OBSERVATION XXIV: A FUNCTIONING ANARCHY
OBSERVATION XXV: A FUNCTIONING ANARCHY JUSTIFIED BY DOCUMENTATION
THE ENVIRONMENT VISITED VI: THE ARISTOCRACY OF VERIFIERS
THE ENVIRONMENT VISITED VII: NONDETERMINISM & PARTIAL UNDECIDABILITY
THE ENVIRONMENT VISITED VIII: NONDETERMINISM OF ALL TYPES IS A WAY OF LIFE
THE ENVIRONMENT VISITED IX: THE FURTHER RELEVANCE OF THE IP=PSPACE MODEL
THE ADVENT OF THE GLOBAL VILLAGE I: THE QUEST FOR THE MEMEX
THE ADVENT OF THE GLOBAL VILLAGE II: THE NEED FOR MASSES OF VERIFIERS
THE ADVENT OF THE GLOBAL VILLAGE III: THE FISH TAKE TO THE WATER
THE ADVENT OF THE GLOBAL VILLAGE IV: FIREFLIES BEFORE THE STORM?
THE ADVENT OF THE GLOBAL VILLAGE VI: THE EXPLOSION IN THE GLOBAL VILLAGE
THE ENVIRONMENT REVISITED AGAIN: THE SPATE OF REVOLUTIONS
THE SIMPLIFIED MODEL: SOLVERS OF PROBLEMS AND VERIFIERS OF SOLUTIONS
THE PROBLEM FORMULATION: SOLVERS=VERIFIERS?
THE RELEVANCE OF THE EDUCATIONAL PROCESS I: ONLY VERIFIERS NEEDED
THE RELEVANCE OF THE EDUCATIONAL PROCESS II: WHO WANTS SOLVERS?
THE RELEVANCE OF THE GLOBAL VILLAGE I: UPPER AND LOWER END ACTIVITIES
THE RELEVANCE OF THE GLOBAL VILLAGE II: TWO EDUCATIONAL PROCESSESS
THE TWO GOLDEN GOOSES THEORY
THE TWO GOLDEN GOOSES COOPERATE
FATTENING THE GOLDEN GOOSES
THE GOLDEN GOOSES CLAIM TO BE SICK
THE UTOPIAN MODEL FOR THE GOLDEN GOOSES
THE TWO GOLDEN GOOSES MODELLED
THE TWO GOLDEN GOOSES COOPERATE
THE SOLVER OF PROBLEM VANISHES IN SOFTWARE
THE VERIFIER IS SUPREME IS SOFTWARE
EPILOGUE



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PROLOGUE


A Utopian model is needed that can be used in the Global Village for the mass production of Verifiers of solutions.
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THE BIGGER PICTURE OF THE PROBLEM


We can generalize the basic problem to the general environmental cultural, economic and social practices over centuries.
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THE PURPOSE OF THE EDUCATIONAL PROCESS


The purpose of the educational processes involved is to be considered. Is the aim to turn out Verifiers of solutions or Solvers of problems?
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THE ENVIRONMENT I


The Projects of major institutions as reported in the last half a century in the newspapers and other media can be studied.
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OBSERVATION I


The major thrust in the public sector industries, research institutions & government organizations over the last half a century has been to concentrate on Solving small problems and Verifying the solutions of large problems done elsewhere, by a fashionable concept and cover called import substitution.
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OBSERVATION II


Enormous fanfare and credit was claimed for imaginary mega-projects before their implementation, then the actual implementation quietly forgotten.
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OBSERVATION III


This is consistent with the culture of a world of Verifiers where the actual job of solving a problem was not important or considered the work as essentially that of labor.
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OBSERVATION IV


The solution was to be found by somebody in the local environment by 'muddling through' and it would be reused.
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OBSERVATION V


The solution could be imported or adapted by import substitution by the faceless, nameless lower rung minions.
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THE ENVIRONMENT II


In the educational institutions the philosophy of the extraordinarily gifted Macaulay who created the groundwork for the modern educational institutions still prevails.
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OBSERVATION VI


This is oriented to turning out Verifiers of solutions obtained elsewhere and glorified Verifiers of procedures formulated by others.
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THE ENVIRONMENT III


The educational process studied.
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OBSERVATION VII


(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)

The educational process is by and large grossly understaffed.
There is a large section of young self taught, demodulated, disgruntled and grossly underpaid teachers, eyeing the flashy way of life of the outsourcing IT industry.
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OBSERVATION VIII


A radical increase in the materialistic front of a large section of teachers had no effect on the culture. The silent majority prefer to be Lotus Eaters.
There are rare silent exceptions, as out of any chaos stars will be born.
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OBSERVATION IX


(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)

The older faculty by and large still suffer from PC-phobia, mouse mania, keyboard terror and network neurosis.
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OBSERVATION X


The older faculty cannot get over 'typewriter' syndrome. The keyboard is to be used by the typist, stenographer or clerk.
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FROM THE NEWSPAPES
&
BY EXPERIENCE


Mechanical typewriters are still very commonly used in government institutions and the legal profession.
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OBSERVATION XI


The silent majority prefer to be Lotus Eaters which by default is the safest course of action. There are rare quiet, silent exceptions, as out of any chaos stars will be born.
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OBSERVATION XII


They are mainly Verifiers of solutions to problems done elsewhere by somebody else in some other part of the world.
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OBSERVATION XIII


(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)

The explosive growth of knowledge has led to the standard practice, in most educational institutions in the environment, over the last half a century: "If you don't know a subject, then teach it".
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OBSERVATION XIV


A large portion of the material of the Invisible Colleges is either merely adapted or an introduction written for the same, all in the name of the local faculty.
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OBSERVATION XV


This ends up in Verifiers of knowledge and solutions who create Verifiers of solutions.
The silent majority continue to be in an enchanted state in the Continent of Circe.
There are rare quiet, silent exceptions, as out of any chaos stars will be born.
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THE ENVIRONMENT IV


In the formal educational process the teacher is the Verifier of solutions and the student is the Solver of problems. In the coaching industry the roles get reversed. The student is the Verifier of solutions and the instructor the Solver of problems.
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THE ENVIRONMENT V


Out of any chaos stars will be born, but it is not common. Let this be applied to the educational pyramid.
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OBSERVATION XVI


Most of the educational pyramid relies on the collective wisdom of the student community which by and large is left to fend for itself.
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OBSERVATION XVII


In quite a few cases students and faculty only lend their names to an educational institution.
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OBSERVATION XVIII


Bullet proof documentation is normally created. This relates to the simulation of the real or imagined implementation and audit of procedures involved the educational process.
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OBSERVATION XIX


It is to their eternal credit that the students have in their collective wisdom peacefully, creatively and brilliantly found or rather evolved a solution which more or less works.
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THE SOLUTION EVOLVED
AND
FOLLOWED BY THE STUDENTS


Small problems they solve by themselves. The more difficult ones they rely on a book of solutions.
They use the agile methods of realistic, proven guides for examinations which routinely use the same pattern.
They attend coaching classes to obtain the complements of the right solutions to problems.
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THE NET RESULT


They are Verifiers of solutions. This ends up in interactive Verifiers and Solvers.
The latter represented by standard texts, guides and solutions manuals.
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(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)

THE MODEL


We now have the famous result of Computational Complexity that IP=PSPACE. With a wee bit of procrustean treatment it can be applied to the environment.
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PROCRUSTEAN USE OF THE MODEL


The IP refers to the student in the environment who is an Interactive Verifier of Solutions.
The P in the 'IP' refers to a student of average to above average ability.
The PSPACE refers to a Solver who can solve all the problems in the body of knowledge in the syllabus.
PSPACE comprises an upper bound on all the knowledge that can be reasonably mastered.
The P in 'PSPACE' refers to the ease with which the Solver can solve the problems in the syllabus.
The 'SPACE' in PSPACE intuitively, and in a way, allows the Solver of problems, who is actually the rock foundation and pillar of the knowledge, to be exponentially more competent than the student.
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(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)
(O UT OF CHAOS STARS ARE BORN)

THE INFERENCES-I


The average student has magically mastered an enormous amount of knowledge, almost as well as an average student anywhere else as the theorem shows.
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THE INFERENCES-II


PSPACE is a model that represents all the knowledge that can reasonably be mastered by most students in any educational environment, leaving out the uncommonly rare, very extraordinary bunch of students.
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THE INFERENCES-III


The achievement of the students as an Interactive Verifier is remarkable, especially if one notes that PSPACE is closed under complementation and basically not disturbed by nondeterminism.
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THE INFERENCES-IV


The closure of PSPACE under complement indicates that an educational process turning out Solvers of problems basically deals with the same body of knowledge insofar as the average student is concerned.
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THE INFERENCES-V


The fact that PSPACE is not disturbed by nondeterminism shows that both methods, definitions of nondeterminism seem to result in the same body of knowledge being acquired.
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THE INFERENCES-VI


The Verifier of solutions is to acquire the skills of guessing the solution for a problem and Verifying it. This is to tackle nondeterminism.
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THE INFERENCES-VII


The Solver of problems is to acquire the skills of finding the solution, by guessing or more relevantly based on his experience in solving problems and at the same time finding the proof for the same. This is to tackle nondeterminism in another way.
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THE INFERENCES-VIII


The major catch is that the students in the educational process in the environment are great, extremely capable Verifiers of solutions and not Solvers of problems.
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A PHENOMENON EXPLAINED


Students trained as Verifiers of solutions can only guess the solution and verify it.
They cannot come up with a proof for the problem.
Students self-taught/educated/trained as Verifiers of solutions in the environment cannot, even if they are gifted, comfortably come up with proofs for solutions.
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THE INFERENCES-IX


Note here the use of the texts, by the Invisible Colleges, that are internationally proven are used as a rock foundation/ pillars of some area of knowledge.
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THE INFERENCES-X


The reliable texts, by the Invisible Colleges in various areas of knowledge, take the role of interactive Solvers of problems.
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THE INFERENCES-XI


A three tier system is used.
At the back end are the difficult standard texts.
The middle layer consists of the plethora of interpretations, guides, procrustean texts, solution manuals all of varying degree of quality and reliability.
The front end is the exposition to the student in a number of ways.

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THE INFERENCES-XII


The most common method of exposition is recursively by the students to themselves or a mutually recursive method by a group of students among themselves.
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THE INFERENCES-XIII


In infrequent cases we have formal treatment sequentially by an instructor with varying degrees of competence and cultural relevance.
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THE INFERENCES-XIV


The theorem demands the Solver be perfect. If we allow the Solver only to have a high probability of being correct then we have an interesting situation.
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THE INFERENCES-XV


As one goes down the educational pyramid or deviates from the utopian model the situation changes.
In the environment the reliable Solver in the ideal situation is represented by the texts of the Invisible Colleges in their areas.
These are now replaced in stages by less reliable texts.
Then they are replaced by shoddy texts.
Then they are replaced by prescribed shoddy local texts .
Then the texts are dispensed with.
They are replaced by reliable guides.
They are replaced by unreliable guides.
What is the effect of all this?
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THE INFERENCES-XVI


As the quality of the Solver of problems in the theorem of Interactive Verifiers and Solvers goes down the Verifier has to make up the deficit.
The Verifier is forced to become a Solver of problems.
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THE INFERENCES-XVII


The lesser the reliability of the Solver in the theorem more is the requirement on the Verifier of solutions to actually solve the problems.
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THE INFERENCES-XVIII


If the Solver vanishes in the theorem then the educational process becomes one based on Solvers of problems.
However, the formal instructional component will be missing.
The students only lend their name to the concerned educational institution.
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THE INFERENCES-XIX


The student is now left high and dry. He has to fend for himself.
So the student ends up as a mixture of both Verifiers of Solutions and a Solver of problems.
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THE INFERENCES-XX


Thus lesser the reliability of the formal instruction, the coaching, the guides, the solutions manuals, the texts etc. in an environment of an educational process based on Verifiers of Solutions, more is the benefit and challenge to the determined student to develop as a Solver of Problems.
Out of chaos stars are born.
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ANOTHER PHENOMENON EXPLAINED


A naive use of the theorem of Interactive Verifiers and Solvers is to assume that the whole of PSACE is to be covered.
In an educational process only a 'degree' of mastery of part of the knowledge as defined by the syllabus is required.
This allows PSPACE to be replaces by its subsets.
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ANOTHER PHENOMENON EXPLAINED FURTHER


As PSPACE is replaced by smaller and smaller subsets of itself, the requirements on the reliable Solver of problems diminishes.
The Solver can be progressively replaced by texts of lower and lower quality.
The Solver is replaced by whatever the instructor says.
Finally, the Solver is replaced by some 'class notes' of the brighter students in the class.
This explains a reported media complaint by industry that, in many cases, even in top tier institutions in the environment, neither the instructor nor the student is aware of the standard texts or can identify the Invisible Colleges in their areas.
Let us stick to the Utopian model as modeled by the theorem.
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EXTENSIONS TO THE MODEL


The culture of the theorem allows Solvers of problems to attack problems beyond PSPACE but exceptional Verifiers can also attack problems beyond PSPACE.
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THE INFERENCES-XXI


In practice a Verifier of solutions can learn to become a problem Solver and thus compete.
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THE INFERENCES-XXII


The transition to a Solver from a Verifier is not easy, rather exceptional and not the rule.
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THE INFERENCES-XXIII


Out of any chaos stars are born, but this is a rare occurrence.
A phoenix may rise from its ashes, but it is a rare bird.
It is also difficult to find an inverse Ackermann function like me who competes with the Divine Cactus of the desert that blooms once in 700 years.
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OBSERVATIONS FROM ANCIENT HISTORY


During his visit to India in the mid seventies of the last century Prof. C A R Hoare commented on the difficulty of developing large and/or complex software.
This was about half a century ago when the term 'Software Engineering' was just invented.
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THE INFERENCES-XXIV


Half a century ago it was also determined that there was 'no silver bullet' for software.
So what was valid half a century ago on the basic difficulties and approaches are valid today and in the foreseeable future.
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THE INFERENCES-XXV


The only way out for large/complex software was that Solvers of problems of the highest caliber and IQ should think out to the last detail, what is to be done.
Then one should get hold of a mass of Verifiers of solutions, of the highest caliber and IQ possible.
The Verifiers should fill in the details without the slightest deviation being allowed.
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THE INFERENCES-XXVI


This translates into top quality products of the top of the educational pyramid, which seriously implements the educational process, turning out Verifiers of solutions are very much in demand.
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A SITUATION EXPLAINED


The preceding discussion explains why in the outsourcing field, for a quarter of a century predating the mid-nineties of the last century, the IT-labor and Verifiers of Solutions were primarily drawn from the top tier institutions in the environment.
This was when the players in the software outsourcing field were local companies.
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A SITUATION FURTHER EXPLAINED


The preceding discussion also explains why with the advent of offshore outsourcing in the mid-eighties the Verifiers of Solutions were primarily drawn from the top tier institutions in the environment.
This was when the players in the offshore software field were primarily from advanced economies.
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THE INFERENCES-XXVII


Especially high IQ gifted or well-educated, well-trained Verifiers of solutions are very much in demand.
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THE INFERENCES-XXVIII


The requirements of the industry of Verifiers of solution, is much, much greater than that of Solvers of problems.
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THE INFERENCES-XXIX


Headhunters are forced to go into the deep geographical interiors of the environment in search of high IQ competent Verifiers of solutions.
They may be found in educational institutions of doubtful repute, but ostensibly turning out Verifiers of solutions.
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THE INFERENCES-XXX


The global requirement of Verifiers of solutions runs into millions, and the entire spectrum of human IQ is represented, in the demands of industry.
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THE INFERENCES-XXXI


Small reductions in salary and overheads translates immediately into billions of dollars of hard cash being saved in an economy.
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THE INFERENCES-XXXIII


When the Global Village matures the requirement of Verifiers of solutions will be in billions.
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THE INFERENCES-XXXIV


The relevance of an effective functioning educational process in the Global Village oriented to turning out Verifiers of solutions becomes evident.
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THE ENVIRONMENT REVISITED I


Consider the picture of the larger environment. Let an insignificantly minute part of the population be excluded. There are rare exceptions, as out of any chaos stars will be born.
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OBSERVATION I


Over the centuries there was stagnation on the intellectual front, bankruptcy on the materialistic front and a dead end on the spiritual front.
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OBSERVATION II


Over a century ago the cyclone of Science & Rationalism started blowing in.
Then the cyclone of the industrial revolution blew in over the last half a century.
The cyclone of the information revolution blew in over the last two decades.
Added to this was the cyclone of globalization and the cyclone of liberalization over the last two decades.
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OBSERVATION III


In all cases the stoic reaction of the environment to the cyclones was the same. It has been the same reaction over the centuries to "let noble thoughts blow in to us from all sides".
This reaction was essential in the time immemorial "eternal quest" of the environment in the spiritual field. It was now merely extended to temporal concerns.
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THE ENVIRONMENT REVISITED II


The reaction of the average individual or social unit in the environment to a problem was: "somebody must do something." This was the reaction to the massive future shock.
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OBSERVATION IV


If someone solved a problem it was used and reused by everybody.
It was considered a stupid reinvention of the wheel to solve hard problems over and over again, generation after generation.
This is in radical contrast to an educational process concentrating on turning out Solvers of problems.
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OBSERVATION V


Nobody in the environment wanted to be a Solver of problems; everyone was a Verifier of solutions. Everyone wanted someone else to be Solver of problems. This situation was repeated again and again.
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OBSERVATION VI


The entire world was observed. Every activity and any change in the same noted. Everything in the world had its image in the local environment where Verifiers used and checked solutions done elsewhere or by somebody else.
It was a culture populated by Verifiers of solutions who were only prepared to solve small problems, but would verify the solutions of any problem of any size done by others anywhere in the world.
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THE ENVIRONMENT REVISITED III


The regular TV shows in any channel, in any part of the country in any language, show this cultural aspect of Verifiers who learnedly, vigorously and authoritatively evaluate everything other people have done or not done, but will do nothing themselves.
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OBSERVATION VII


They are the aristocrats of the world. They cannot do anything by themselves regardless of the resources supplied.
They can however condescend to use and comprehensively Verify anything and everything done by others, in any environment.
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OBSERVATION VIII


However, when the Verifiers are in ancient Rome they are more Roman than the Romans themselves. The basic multivalued logic based deep cultural foundation sees no contradiction in this behavior.
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THE ENVIRONMENT REVISITED IV


The aim was to find a solution that exists, and is already done by somebody somewhere.
Alternatively the work must be done by others at low cost and it would be Verified and used, or alternatively used and then fully Verified.
The use of anything is basically an exercise in its Verification is what we learn in the software industry.
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OBSERVATION IX


Thus plagiarism was common and considered a normal way of life.
The 'cut & paste' philosophy was considered to be fashionable, natural and pragmatic.
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OBSERVATION X


In the environment of multivalued logic contradictions peacefully coexist.
One can loudly and openly claim to be following the narrow path but actually be rolling smoothly downhill. There are rare exceptions, as out of any chaos stars will be born.
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OBSERVATION XI


The world of Verifiers gives no special credit for Solvers of problems who are considered to be lower down in the hierarchy. In industry, research, government, education and perhaps in all areas, projects are done by one person for another, or openly purchased in the grey market without any severe backlash. Multivalued logic allows one to claim originality of the work without battling an eyelid. There are rare exceptions, as out of any chaos stars will be born.
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OBSERVATION XII


The world of Verifiers gives no special credit for Solvers of problems who are considered to be lower down in the hierarchy.
Plagiaries or altered theses are written by one person for another surreptitiously in the educational field. Again multivalued logic allows the environment to basically have a warehouse of Nelson's eyes. There are rare exceptions, as out of any chaos stars will be born. The silent majority remain Lotus Eaters.
It is a very common situation for head of an organization, institution or department to demand theses, research articles to be written in his/her name.
It is considered to be a normal, respectable and useful activity.
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OBSERVATION XIII


The world of Verifiers gives no special credit for Solvers of problems who are considered to be lower down in the hierarchy.
Student assignments are in many cases routinely reused with everyone expected to see no evil, hear no evil and say no evil.
Reuse of material in cyberspace, without the reinvention of the wheel, is looked upon as a routine, normal and expected 'smart' activity.
Again the accepted multilogic tolerant environment smoothly allows everyone to be happy.
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OBSERVATION XIV


There are many exceptions to the above, as out of any chaos many small stars will also be born.
The are many who prefer to be Lotus Eaters.
Many prefer to live lost in the enchantment of the Continent of Circe.
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OBSERVATION XV


Multivalued logic based environments allows one to claim be Dr Jekyll publicly and also evidently be Mr. Hyde simultaneously. A normal polite behavior expects no notice to be taken of the latter by verbalization.
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OBSERVATION XVI


The world of Verifiers gives no special credit for Solvers of problems who are considered to be lower down in the hierarchy.
Many research publications are either plagiarized or a simple homomorphism, or verification of results of the original paper. It could be guesswork based on simple permutations and combinations of the results of others. It could be procrustean extensions of work already done.
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OBSERVATION XVII


There are rare exceptions, as out of any chaos stars will be born. In all cases rigid adherence to verifying procedures is found in the documentation involved recording the activity. The Verification is perfect.
In all cases the multivalued based environment allows the persons involved to claim originality as fundamental in their life. This claim is made without battling an eyelid.
There are rare exceptions, as out of any chaos stars will be born.
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THE ENVIRONMENT REVISITED V


The idea of not reusing something/everything and trying to do it on one's own was considered to be a ludicrous activity involving reinvention of the wheel.
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OBSERVATION XVIII


The tears, toil, sweat and cost of doing something and Solving problems was avoided.
The more feudal landed aristocratic mindset of Verifying by using what others, the peasants & workers, have toiled & done was preferred.
The aim was to Verify the work turned out by the labor, just like any Supervisor or Manager or Auditor or Customer in the industrial environment.
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OBSERVATION XIX


In parts of the environment the agrarian revolution is new, and the barter based feudal culture still prevails.
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OBSERVATION XX


In the environment the person doing the work and the person taking the credit for it are normally different.
After all, throughout the history of the human race, it has always been the Divine Right of the aristocrat to Verify and take credit for the work of his minions.
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OBSERVATION XXI


In a feudal environment a minion should not exceed his limits.
His duty is to hand over the results of his labor to the aristocrat, who by Divine Right will Verify and enjoy the fruits of the same.
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OBSERVATION XXII


Going further a group of aristocrats can wage a bitter war over taking credit for some Verified something (which they need not understand).
Some minions have labored and Verified that something.
It is the Right of Conquest that finally determines who gets the credit for that Verified something.
This was in education, research, industry and perhaps all walks of life. There are rare exceptions, as out of any chaos stars will be born. This was the world of the Verifiers.
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OBSERVATION XXIII


This sometimes ended up in ludicrous situations.
Credit was taken by some feudal heads of organizations and local quislings for original groundbreaking work.
The long suffering students had the last laugh.
The credit was based on activity done elsewhere by leading authorities and luminaries, who suddenly wake up and start crying foul.
This was done to such an extent that at times it became an obscene affair.
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OBSERVATION XXIV


The environment has been likened by independent observers as a functioning anarchy.
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OBSERVATION XXV


It can be noted that it is a functioning anarchy of disciplined Verifiers of solutions, who are very rigid on real/imagined procedural matters being recorded without flaws.
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THE ENVIRONMENT REVISITED VI


For centuries the princely class, the landed aristocracy, the bankrupted aristocracy and the upper part of the pyramid of social stratification were a hereditary class of Verifiers of solutions, verifying the work of hordes of minions i.e. the Solvers of problems.
Thus being a Verifier of solutions was socially superior to being a plebian Solver of problems.
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THE ENVIRONMENT REVISITED VII


In the environment a multivalued logic based lifestyle was essential for survival.
Nondeterminism and partial undecidability are a way of life.
All shades of nondeterminism prevail.
In the environment one never really can predict an event, one waits till it occurs and then it is known.
The traditional culture of the environment to rely on a hierarchy of oracles, or family astrologers, seems to parallel the use of the power of oracle machines in the Theory of Computation.
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THE ENVIRONMENT REVISITED VIII


The search for any address normally and invariably involves nondeterminism. Nondeterminism, with all its variants, is taken for granted in the anarchy in the environment in daily life, e.g. finding one's way through the chaotic traffic, keeping an appointment, some person honoring a commitment, random social and political unrest etc. etc.
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THE ENVIRONMENT REVISITED IX


In general one has to rely on a high probability of something happening the way one wants it to happen.
In such a situation the relevance of the IP=PSPACE model becomes more evident.
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THE ADVENT OF THE GLOBAL VILLAGE-I


Into this culture the Global Village appeared from nowhere, created by a culture of Solvers of problems.
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THE ADVENT OF THE GLOBAL VILLAGE-II


The culture of the monied Solvers of problems wanted to solve larger and larger problems and mega-problems.
They needed masses and masses of Verifiers, of varying degrees of capability, at reasonable rates.
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THE ADVENT OF THE GLOBAL VILLAGE-III


The culture and economic situation of Verifiers was ripe and equal to the occasion and took to it like a fish to water.
This was extended to all activities and knowledge areas.
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THE ADVENT OF THE GLOBAL VILLAGE-IV


For any activity, at any price, there were masses of Verifiers ripe and ready.
If not ready the culture and the business practices of fly-by-night operators in the environment allowed them to rapidly mushroom.
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THE ADVENT OF THE GLOBAL VILLAGE-V


Another view is that they were suddenly created like fireflies before a storm to cater to the requirements of another horde of fireflies before a storm in distant cultures.
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THE ADVENT OF THE GLOBAL VILLAGE-VI


A revolution and explosion took place in the Global Village.
Everybody stared in utter disbelief.
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THE ENVIRONMENT REVISITED AGAIN


This perhaps is a simplified view.
One should consider the limitations of opportunities caused by social stratification, the availability of a large young work force of all degrees of capability, the foresight of Macaulay, the half a century effect of the Nehruvian socialistic-democratic functioning in the environment, the spiritual dead end, the experimentation with Science and Rationalism, the energetic but ill-fated self-reliance based efforts of half a century, the lure of materialism, the temptation of a new lifestyle radically different from that of a feudal agrarian environment, leapfrogging the industrial revolution, leapfrogging the agrarian revolution, the sudden simultaneously occurring access to the large scale benefits of the consumer, industrial, information, information technology, transportation and communication revolutions.
Added to this were the sudden liberalization and globalization revolutions.
To this should be added the international financial bubbles, the Y2K and dot com bubbles, the software crisis bubble, the maintenance iceberg bubble, the unlimited financial greed bubble of industry, the real estate bubble, the education bubble, etc. etc......
To this should be further added the ease of Verifiers of solutions enjoying the facilities of advanced infrastructures, social fabrics, rule of law and economies of industrialized countries, etc. etc.
All the above rushed into the centuries old peaceful life of many millions to a billion people (Lotus Eaters?) in the space of a few years.
The negative and positive effects of the chaos that resulted from all the above rushing into a vast vacuum that existed for centuries, in the short span of time of a few years cannot really be explained. A few decades or centuries must pass before the effect is fully understood. What is more likely is that it will just be forgotten as normal with any natural or human (temporal or spiritual) cyclonic disturbance in the time immemorial ahistorical culture of the environment.
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THE SIMPLIFIED MODEL


However, let us take the view that the basic resource was the easy availability of employable competent Verifiers of solutions drawn from a centuries old culture of Verifiers.
This economically satisfied the urgent employment opportunities of Solvers of problems drawn from a centuries old culture of Solvers.
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THE PROBLEM FORMALISED


We thus have an instance of the famous Solvers=Verifiers or Provers=Verifiers or by a procrustean restriction the P=NP problem staring at us!!! Let us elaborate on this.
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THE RELEVANCE OF THE EDUCATIONAL PROCESS
OF
THE ENVIRONMENT - I


The problem is the culture of the environment, and the purpose of the educational process.
In reality it is only easily employable Verifiers that are to be turned out.
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THE RELEVANCE OF THE EDUCATIONAL PROCESS
OF
THE ENVIRONMENT - II


The problem seems to be that one considers that the grass is greener on the other side and wants Solvers of problems to be turned out to aid some other culture or educational process.
This without changing the culture of the environment or the educational process.
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THE REQUIREMENTS
OF
THE GLOBAL VILLAGE - I


The situation for the Global Village is very bright.
From the industry point of view the above says that the aim should be clear.
Are we aiming for the lower end activities of the product life cycle or the upper end activities?
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THE REQUIREMENTS
OF
THE GLOBAL VILLAGE - II


From the perspective of the Global Village, there seem to be two educational processes involved which are of relevance.
One turning out Verifiers of solutions and one Solvers of problems.
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THE TWO GOLDEN GOOSES THEORY


There are two Golden Gooses operating in the Global Village that resulted from the half century long 'crusades' in quest of the Memex.
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THE TWO GOLDEN GOOSES COOPERATE


They are at present harmoniously cooperating in their distinct spheres of operation, to ensure the future effective functioning of the Global Village.
The sets of Verifiers and Solvers are disjoint, contented with their lot, and not trying to enter each others spheres.
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FATTENING THE GOLDEN GOOSES


The solution is not to kill one of them but to fatten them, globalize them, realistically regulate them, culturally adapt them by localization and let them harmoniously cooperate and coexist.
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THE TWO GOLDEN GOOSES IMAGINE THEY ARE SICK


They both seem to be showing serious signs of sickness, starvation and demotivation, and assuming either that the grass is greener on the other side or that the other side is responsible for the problems faced.


THE UTOPIAN MODELS OF THE GOLDEN GOOSES


Let both the educational processes be considered in their Utopian models.
One is based on Solvers of problems and the other on Verifiers of solutions.
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THE TWO GOLDEN GOOSES MODELLED


Depending on the context the roles of who turns out the personnel for the upper end functions and who for the lower end functions of some activity differs.
In any activity the Solvers and Verifiers have to harmoniously cooperate with each other.
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THE TWO GOLDEN GOOSES COMPARED


Are the two different when their ideal Utopian models are considered?
Are they basically equal?
Is one really superior to the other?
What is the situation when taken to the extreme?
This is the famous open problem of computer science and mathematics.
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THE SOLVER OF PROBLEMS VANISHES


When one considers the world of the Solvers of problems they have also ended up in intellectual knots.
It turns out that when it comes to computation and software for some real life application there is no such thing as a Solver of problems , only Verifiers of solutions exist.
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THE VERIFIER IS SUPREME


The Solver does not exist.
The Verifier is supreme.
The "upper end" Verifier.
The "lower end" Verifier.

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EPILOGUE


Only Verifiers are needed for software/computation: the upper end activities decide how to go about it and the lower end activities do it.

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START OF STRAY THOUGHTS


SOLVER!!! SOLVER!!! SOLVER!!! SOLVER!!! SOLVER!!! SOLVER!!! SOLVER!!! SOLVER!!! SOLVER!!!




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PREAMBLE
CRACKING COMPETITIVE EXAMINATIONS
THE “SILVER BULLET” IN COMPETITIVE EXAMINATIONS
THE GOOD PART OF COACHNG SHOPS
THE WORLD OF MULTIPLE CHOICE EXAMINATIONS
THE WORLD OF VERIFIERS OF SOLUTIONS
THE WORLD OF SOLVERS OF PROBLEMS
THE WORLD OF COMMON SENSE AND COMPUTATION
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I. SOLUTIONS TO PREVIOUS GATE THEORY OF COMPUTATION PAPERS.

II. THEORY OF COMPUTATION QUESTION BANK

III. ALGORITHMS FOR GATE

IV. QUESTIONS IN LANGUAGE PROCESSORS FOR GATE

V. FAIRY TALES AND INTRACTABILITY

VI. METAMATHEMATICS FOR PRIMARY SCHOOLS

VII. METAMATHEMATICS FOR DUMMIES
VIII. ALGORITHMS FOR DUMMIES--PPTs

IX. COMPUTER SCIENCE LITERACY IN PRE-AGRARIAN AND TRIBAL SOCIETIES

X. COMPUTER SCIENCE LITERACY IN PRIMITIVE SOCIETIES

XI. DISCUSSION ON ALGORITHMS

XII. INTRACTABILITY FOR PRIMARY SCHOOLS

XIII. THEORY OF COMPUTATION MADE EASY

XIV. THEORY OF COMPUTATION FOR SECONDARY SCHOOLS

XV. PROVEN NOTES & QUESTION BANK IN THETHEORY OF COMPUTATION

XVI. SERIOUS DISCUSSION FORUM

XVII. INTRACTABILITY MADE EASY

XVIII. CRACKING COMPETITIVE EXAMINATIONS

XIX. THE “SILVER BULLET” IN COMPETITIVE EXAMINATIONS

XX. THE GOOD PART OF COACHNG SHOPS

XXI. THE BAD PART OF COACHING SHOPS

XXII. PREAMBLE TO A FORMAL STUDY OF MULTIPLE CHOICE BASED COMPETITIVE EXAMINATIONS

XXIII. THE WORLD OF MULTIPLE CHOICE BASED EXAMINATIONS

XXIV. THE WORLD OF VERIFIERS OF SOLUTIONS

XXV. THE WORLD OF SOLVERS OF PROBLEMS

XXVI. THE WORLD OF COMMON SENSE AND COMPUTATION

XXVII. THE WORLD OF NEGATIVE THOUGHTS AND COMPUTATION

XXVIII. INTRACTABILITY AND COMMON SENSE

XXIX. COMPUTER SCIENCE LITERACY IN FEUDAL SOCIETIES

XXX. COMPUTER SCIENCE LITERACY IN RURAL SOCIETIES WITH TRACES OF THE INDUSTRIAL REVOLUTION








PART III
THE WORLD OF SOLVERS OF PROBLEMS





METAMATH EMATICS
SIX BLIND MEN AND THE ELEPHANT

SIX BLIND MEN AND THE ELEPHANT

SIX BLIND MEN AND THE ELEPHANT




METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
O NE BLIND M AN LEADIN G ANOTHER
SIX BLIND MEN AND THE ELEPHANT



METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
O F THE DUMM IES
FOR TH E DUMMIES
BY THE DUM MIES




CONTEN TS

THE STATEMENT OF THE PROBLEM
THE EMPEROR INITIATES STEPS FOR A SOLUTION
THE PRIME MINISTER IS FRIGHTENED
THE STRATEGY FOR A SOLUTION
THE OTHER USES OF THE SOLUTION
STILL OTHER USES OF THE SOLUTION
THE COURTIERS SING A SONG
THE SEARCH FOR THE SOLVER
THE SOLVER ENTERS THE STAGE
THE STRATEGY OF THE SOLVER
THE METHODS OF THE SOLVER
THE NEW BED OF PROCRUSTES THE SOLVER
THE SOLVER IS EMPLOYED
THE EASY PART OF THE SOLUTION
THE STRATEGY FOR GEOMETRY
THE HARD PART OF THE SOLUTION
PROCRUSTES TACKLES THE VOID
POINTS DO NOT EXIST IN THE CONTINUUM
THE CREATION OF A POINT
ENTER ARISTOTLE
THE EXPULSION OF THE CRETEAN
PROCRUSTES AND THE SERPENT
PROCRUSTES CREATES POINTS IN THE CONTINUUM
PROCRUSTES AND HIS PIGGY BANK
PROCRUSTES INVENTS THE NATURAL NUMBERS - I
PROCRUSTES DREAMS OF THE OVERLOADED CAMEL
PROCRUSTES INVENTS THE NATURAL NUMBERS - II
PROCRUSTES CREATES THE INTEGERS AND OPERATIONS ON THEM
THE SUPERNATURAL PROPERTIES OF THE INTEGERS
OPERATION ON INTEGERS
PROCRUSTES STARTS COUNTING
PROCRUSTES AND THE TORTOISE
THE ARGUMENTS OF THE TORTOISE - I
THE ARGUMENTS OF THE TORTOISE - II
THE ARGUMENTS OF THE TORTOISE - III
THE ARGUMENTS OF THE TORTOISE - IV
THE ARGUMENTS OF THE TORTOISE - V
THE TORTOISE IS PUNISHED
PROCRUSTES BEGS THE QUESTION
PROCRUSTES VISITS THE BOTTOMLESS PIT
PROCRUSTES TAMES THE INFINITIES
PROCRUSTES REACHES INFINITY
PROCRUSTES IN THE CIRCUS
THE PROPERTIES OF SETS
THE ROYAL BARBER OBJECTS
PROCRUSTES TAMES MATHEMATICS
ANALYSIS IN THE BED OF PROCRUSTES
MATHEMATICS IN THE BED OF PROCRUSTES
THE SUPPRESSION OF DISSENT
THE CANNIBALS ARE EXCITED
THE CANNIBALS ARE CONFUSED
PROCRUSTES LAUNCHES THE WORLD WARS
PROCRUSTES DEFINES COMPUTATION
THE CREATION OF A MONSTER
THE MONSTER AS DR JEKYLL
THE MONSTER ENGAGES ITSELF
THE METHODS OF THE MONSTER
THE MONSTER AS MR HYDE
THE MONSTER AS A SUPERNATURAL
THE MULTI-HEADED MONSTER
ARCHIMEDES COUNTS THE HEADS OF THE MONSTER
THE BOTTOMLESS PIT OF THE MONSTER
THE FOOD OF THE MONSTER
THE MONSTER IS ETERNALLY ACTIVE
THE MONSTER IS A LINGUIST
THE MONSTER AND SYMBOLISM
THE MONSTER IS A SCHOLAR
THE MONSTER CHALLENGES ALL SEARCH ENGINES
THE MONSTER AND GOOGLE
COOKING FOOD FOR THE MONSTER
EDIBLE FOOD FOR THE MONSTER
THE MONSTER AS A CANNIBAL
THE MONSTER SOLVES THE PROBLEMS OF INDUSTRY
THE MONSTER AS THE IDEAL CUSTOMER
THE FINANCES OF INDUSTRY BECOME SOUND
THE COLLECTION AGENTS ARE OUT OF BUSINESS
PROCRUSTES DEFINES EFFECTIVE COMPUTATION
MODELS FOR EFFECTIVE COMPUTATION
THE MONSTERS LOVE THEMSELVES
THE MONSTER CAN REPRODUCE ITSELF
THE MONSTER OF MONSTERS
THE MONSTER OF MONSTERS SETS AN EXAMPLE -- I
THE MONSTER OF MONSTERS SETS AN EXAMPLE -- II
THE MONSTER OF MONSTERS SETS AN EXAMPLE -- III
THE MONSTER OF MONSTERS SETS AN EXAMPLE -- IV
THE MONSTERS GET INTO A LOOP
THE MONSTERS ARE STUMPED -- I
THE MONSTERS ARE STUMPED -- II
THE MONSTERS ARE STUMPED -- III
THE MONSTER OF ALL MONSTERS LOVES ITSELF
THE MONSTERS CONTINUE TO LOVE THEMSELVES
THE MONSTERS KEEP ON LOVING THEMSELVES
PROCRUSTES CONSULTS ORACLE AFTER ORACLE
THE FINAL SOLUTION
PROCRUSTES WANTS A MEDAL
PROCRUSTES DECAMPS
PROCRUSTES RESURFACES
THE MONSTER IS CONFUSED
THE FAMOUS PROBLEM
ATTEMPTS TO SOLVE THE PROBLEM
DENYING THE PROBLEM
USING PROCRUSTEAN MATHEMATICS FOR A SOLUTION
THE DANGERS OF SIMULATION
THE SOLVER DOES NOT EXIST
THE DIFFICULTY OF PROVING THE EXISTENCE OF A SOLVER
THE SOLVER OF PROBLEMS MAY EXIST AFTER ALL
THE VERIFIER IS SUPREME
RESTATEMENT OF A FAMOUS PROBLEM
THE SOLUTION TO THE PROBLEM
THE USE OF THE SOLUTION
SOLACE AND CONSOLATION
THE EMPEROR'S ROYAL PROCESSION
EPILOGUEC



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A hypothetical, naive, simplistic, procrustean model using specious metamathematics


METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
O F THE DUMM IES

FOR TH E DUMMIES

BY THE DUM MIES

SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER





PROLOGUE


When we were in our centuries of sleep an interesting thing happened in the world. In a far off land about two centuries ago a delegation of children led by Winnie the Pooh and Tigger met the Emperor.
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THE STATEMENT OF THE PROBLEM


They complained about the horrid mathematics subject they had to study and the birch of the mathematics teacher. The Emperor recalled having had similar problems when he was young.
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THE EMPEROR INITIATES STEPS FOR A SOLUTION

The Emperor was pleased to order the Prime Minister to find a Solver for a permanent solution with the rider that he (i.e. the Emperor), the children and their leaders would be Verifiers of the solution.
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THE PRIME MINISTER IS FRIGHTENED


The Prime Minister was frightened. The Emperor may cut off his head if he failed. He asked the courtiers for help.
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THE STRATEGY FOR THE SOLUTION

A suave courtier suggested the strategy for a solution.
Like the alchemists of old had tried to do in their area mathematics had to be distilled and its essence found. This could be encapsulated and converted to a sugar coated pill. The pill could be swallowed with milk and honey. The mathematicians and mathematics teachers can be shown the door. A mathematics teacher can be left in the wilderness to use his birch on himself.
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THE OTHER USES OF THE SOLUTION

Another suave courtier convinced everyone that the mathematics pill will explain all the mysteries of the Universe and the High Priest and his minions can be bundled off. The High Priest could be left in the desert and can listen to his own sermons.
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STILL OTHER USES OF THE SOLUTION

Another suave courtier convinced everyone that the mathematics pill will explain all the mysteries of sickness. The horrid Royal Physician and his minions can be expelled. The Royal Physician could be left in the Artic wilderness and can swallow his own bitter medicines, to heal himself.
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THE COURTIERS SING A SONG

The courtiers went on and on. They were all in the pay of a foreign scoundrel.
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THE SEARCH FOR THE SOLVER

A high power Search Committee was formed and messengers were sent full speed in all directions to find the Solver.
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THE SOLVER ENTERS THE STAGE


Half a century later a legendary scoundrel named Procrustes descended from the legends of ancient Greece and entered Mathematics with an aim to reform it, distill it, get its essence and create the sugar coated pill.

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THE STRATEGY OF THE SOLVER


Procrustes had a reputation for having a magic bed which he said would fit anyone.

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THE METHODS OF FOR THE SOLVER

Procrustes seems to have taken a leaf out of a course in Programming Languages. If a person was bigger than the bed he employed 'narrowing' and lopped of the limbs etc. till the person could fit his bed. If a person was too short he employed 'widening' and stretched the person's limbs so that he could fit into his bed.

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THE NEW BED OF PROCRUSTES THE SOLVER

Procrustes now had a new bed which he called Arithmetic and claimed all mathematics would fit into it.

METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
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THE SOLVER IS EMPLOYED


Procrustes was employed by the Emperor on the recommendation of the courtiers and charged with the task of taming mathematics. He was to be paid a penny a day for his efforts. He was given a Piggy Bank to store his money.

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THE EASY PART OF THE SOLUTION


Procrustes left Algebra and Geometry alone. Much to his disgust a century of effort by the mathematicians he had employed showed that Algebra & Geometry could be put into various knots & contortions and actually fit into his bed.
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THE STRATEGY FOR GEOMETRY



Geometry did create some trouble, till one used the ancient proverb: "Once a goon always a goon".
In any Geometry there are invariants which do not basically result in any change to a goon when applied to the goon. Once these are isolated it is seems possible to reduce that Geometry to Arithmetic.
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THE HARD PART OF THE SOLUTION


Analysis was a troublesome affair. It depended on the continuum which seemed to be a model for the Universe.
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PROCRUSTES AND THE VOID

Procrustes started with the Void as the Universe. By 'narrowing' he declared the Universe is the Void.
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POINTS DO NOT EXIST IN THE CONTINUUM

Procrustes widened the Universe to a massive lump where there was no such thing as a point.
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THE CREATION OF A POINT

By 'narrowing' Procrustes reduced the Universe to a mathematical point. By 'widening' he said this point was eternal, immortal but dumb. It could not do anything by itself.
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ENTER ARISTOTLE


Procrustes 'narrowed' the concept of differing points of view allowed to the human race to two valued logic, putting the blame on Aristotle. He claimed that for every statement he was correct and the other person wrong.
By 'narrowing' he did not allow suo motto change by the immortal truth values for an eternal amount of time.
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
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THE EXPULSION OF THE CRETEAN


The ancient ambassador from Crete had serious objections on this two valued logic business. He was promptly expelled to ancient Crete to eternally contemplate on the validity of his objections.

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PROCRUSTES AND THE SERPENT

Procrustes had a frightening dream. He saw a fearful spotted Snake in the continuum. He woke up with a Divine Inspiration and by 'narrowing' claimed there was something called a real number line/curve in the continuum.
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PROCRUSTES CREATES POINTS IN THE CONTINUUM

Procrustes considered the Universe of the single eternal, immortal, dumb point. He 'widened' it to an infinite collection of distinct eternal, immortal, dumb points. By 'narrowing' he did not allow suo motto birth, death or change in any point.
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PROCRUSTES AND HIS PIGGY BANK

Procrustes had a dream that he was taking stock of his piggy bank where he kept his pay.
Starting with a penny, he kept on adding another penny as a successor, and found out that he had progressively increasing small but tidy sum.
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PROCRUSTES INVENTS THE NATURAL NUMBERS-I

Procrustes woke up with a Divine Inspiration that God created the natural numbers and all else is the work of Procrustes.

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PROCRUSTES DREAMS OF THE OVERLOADED CAMEL

Procrustes had a dream that he was in the desert. He saw a camel with a heap of straw on its back. Its master kept on adding straw after straw to the load on the back of the camel. Nothing seemed to happen to the camel.
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PROCRUSTES INVENTS THE NATURAL NUMBERS-II



Procrustes woke up with a Divine Inspiration that God created an infinite 'bunch' the natural numbers and all else is the work of Procrustes.

METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
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PROCRUSTES CREATES THE INTEGERS AND OPERATIONS ON THEM



Procrustes applied his dream.
Starting with a single immortal, eternal, dumb integer representing the Universe by 'widening ' he created an unlimited number of immortal integers.
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THE SUPERNATURAL PROPERTIES OF INTEGERS

He 'widened' the integers and declared they were immortals and eternal. By 'narrowing' he did not allow birth, death, suo motto changes.

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OPERATIONS ON INTEGERS

He 'widened' many operations on integers and declared by 'narrowing' that they and their results could be defined. He used 'widening' to declare that they were immortal and eternal entities.
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PROCRUSTES STARTS COUNTING


He 'narrowed' the collection of points in the continuum and said it consisted of distinct points that could be described by 'bunches' of integers or combinations of them. By 'narrowing' he did not allow suo motto change by the immortal points for an eternal amount of time.
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PROCRUSTES AND THE TORTOISE

Procrustes dreamt that he saw a person called Zeno traveling on a tortoise. The tortoise claimed that the points in the continuum cannot be assigned numbers, or 'bunches' of numbers.
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THE ARGUMENT OF THE TORTOISE - I

The tortoise could never travel to any point from any other point, by traveling a fraction of the remaining distance in a stage of its journey.
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THE ARGUMENT OF THE TORTOISE - II

The tortoise claimed that in an suitably overcrowded metropolis everyone's house extends and includes his neighbor’s houses in all directions.
This was the situation in the continuum. Every point includes all the points adjacent to it. Any mapping to integers will show that.
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THE ARGUMENT OF THE TORTOISE - III

The continuum cannot be described by natural numbers or integers.
This was the stand of the tortoise.
There is only one house in a suitably overcrowded metropolis, and thus just one point in the continuum.
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THE ARGUMENT OF THE TORTOISE - IV

There is no such thing as infinity claimed the tortoise.
Only a finite number of natural numbers and integers exist.
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THE ARGUMENT OF THE TORTOISE - V

The tortoise threatened to descend into the Empire and complain to the Emperor that Procrustes was all bogus.
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THE TORTOISE IS PUNISHED

The tortoise was banished to hold up the entire Earth on its back eternally.

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PROCRUSTES BEGS THE QUESTION

Procrustes further 'narrowed' the points in the continuum to a class of immortal 'computable' real numbers. By 'narrowing' he did not allow suo motto change by the 'computable' real numbers for an eternal amount of time.
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PROCRUSTES VISITS THE BOTTOMLESS PIT


Procrustes had a dream that he was cast into the Bottomless Pit. Hurling down the pit he met friendly Titans who were also hurling down the pit. They would hurl down for an infinite amount of time, throughout eternity. He found out that they were basically a friendly, simple lot who had been taken for a ride by some unscrupulous youngsters.
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PROCRUSTES TAMES THE INFINITIES

Procrustes woke up and claimed Divine Inspiration insofar as infinity was concerned.
He 'narrowed' infinity and reduced it to some kindly, harmless, naive, simple old persons next door. They were simple persons, perhaps a little foreign, but just like us. By 'narrowing' he did not allow suo motto changes by any of the infinities for an eternal amount of time.

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PROCRUSTES REACHES INFINITY

Procrustes dreamt his pennies were adding up. It was just a matter of time till his Piggy Bank reached, overtook Croseus and then reached some infinity.
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PROCRUSTES IN THE CIRCUS


Procrustes dreamt that the Emperor had thrown him into he Arena. Herds & herds of herds, of wild animals were chasing him.
He woke up and claimed that by Divine Inspiration there were some things called 'sets' which were fundamental to all mathematics.

METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
SI X BL I ND M EN AN D T HE ELEPHANT
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THE PROPERTIES OF SETS

Procrustes 'narrowed' the concepts of sets and operations on them till they behaved themselves, and 'widened' their attributes by granting them immortality.
By 'narrowing' Procrustes did not allow suo motto change by sets at any time throughout eternity.
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THE ROYAL BARBER OBJECTS


The royal Barber of all Barbers had some serious objections. He was promptly banished to the desert to eternally contemplate on the dignity of shaving himself.

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PROCRUSTES TAMES MATHEMATICS


Procrustes now said by 'narrowing' that what was left of the butchered universe, the 'bunch' of immortal points described by his contortions of integers and sets of integers was all that mattered.

METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
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ANALYSIS IN THE BED OF PROCRUSTES

He had thus by 'narrowing' reduced the universe and hence the continuum to computable real numbers, and hence to integers, and hence Analysis was reduced to arithmetic.
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MATHEMATICS IN THE BED OF PROCRUSTES

So now he had put the lid on mathematicians & mathematics and reduced everything to Arithmetic.

METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
SI X BL I ND M EN AN D T HE ELEPHANT
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
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THE SUPPRESSION OF DISSENT


There were some complaints on the way the continuum was butchered and the cavalier treatment of infinity did not go down well in some quarters. However, dissent was put down with a strong hand.

METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
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THE CANNIBALS ARE EXCITED


The cannibals at the edge of the Empire were excited when they saw the butchered continuum. They gave it a choice between being roasted alive or boiled alive.
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THE CANNIBALS ARE CONFUSED

The Cannibals had a strong lobby, but Procrustes managed to put them into an eternal loop. They were left to eternally contemplate on the confusion he created in their confused minds.
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PROCRUSTES LAUNCHES THE WORLD WARS


One thing leads to another, perhaps unintended consequences. A hypothetical view can be taken, that this Denial of the continuum and 'narrowing' of infinity, resulted in the human race merrily rolling downhill for half a century.
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PROCRUSTES DEFINES COMPUTATION


Procrustes 'narrowed' the purpose of the Universe to something indulging in 'computation' describable by arithmetic and hence encompassing mathematics.
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THE CREATION OF A MONSTER


Procrustes created an unspeakable horror called the Turing machine to frighten future generations of naughty children.

METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
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THE MONSTER AS DR.JEKYLL


A first acquaintance with the Dr Jekyll like machine gave it naive, user friendly toy like characteristics. It seemingly had a kindergarten type vocabulary, literacy and manipulative ability.
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THE MONSTER ENGAGES ITSELF

The monster indulged in simple activities like simulating picking up the Pacific Ocean and transferring it to the Atlantic Ocean.
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THE METHODS OF THE MONSTER

The monster used a thimble to simulate the transfer of water: a thimbleful of water at a time.
It carried on the process for eons of time.
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THE MONSTER AS MR. HYDE


Procrustes exhibited its true Mr. Hyde character.
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THE MONSTER AS A SUPERNATURAL

Procrustes 'widened' the capabilities of his machine by endowing it with immortality, infinite reliability, and the ability to compute eternally, much beyond Odin's feast or Shiva's dance of Death.
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THE MULTI-HEADED MONSTER

It could by metamorphosis convert itself into a multi-headed hydra or a ferocious multi-headed demon descending directly the from myths and legends, of many cultures the world over.
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ARCHIMEDES COUNTS THE HEADS OF THE MONSTER

The number of heads and their associated tapes could be more than the number of grains of sand Archimedes estimated to be in all the beaches of the world.
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THE BOTTOMLESS PIT OF THE MONSTER

The monster had a digestive system that was a bottomless pit for a never ending, voracious consumption of food.
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THE FOOD OF THE MONSTER

The monster had a very simple staple diet of ink and tape.
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THE MONSTER IS ETERNALLY ACTIVE

The monster did not require any energy for its operation, unlike the voracious demands for power of other computing devices like a Google server farm.
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THE MONSTER IS A LINGUIST

The monster was comfortable with all the symbols of all languages in the world, past, present and the foreseeable future.
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THE MONSTER AND SYMBOLISM

The monster was comfortable with all the symbols of all the cultures, past, present and the foreseeable future.
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THE MONSTER IS A SCHOLAR

The monster had a finite control which could store the entire library of Alexandria, all the libraries of the world, all the information, knowledge and associations of the human race in the past, present and possible future.
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THE MONSTER CHALLENGES ALL SEARCH ENGINES

The monster could organize, store and retrieve this information from its finite control with a speed surpassing that of light, in fact instantaneously.
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THE MONSTER AND GOOGLE

The monster should make any Google search engine, past, present or future end up with a strong inferiority complex.
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COOKING FOOD FOR THE MONSTER

Procrustes used 'widening' to allow any entity to be encoded as a symbol or sequence of symbols even if the entity had immortal, eternal or infinite characteristics.
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EDIBLE FOOD FOR THE MONSTER

By 'narrowing' Procrustes demanded the sequence represent a sequence computable by his machines.
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THE MONSTER AS A CANNIBAL

In particular his machines could be encoded as a sequence of symbols.
This sequence could be fed to his machine.
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THE MONSTER SOLVES THE PROBLEMS OF INDUSTRY


Procrustes 'widened' the capabilities of all industries & businesses, of all civilizations and cultures the world over, from cottage industries to MNCs, from supermarkets to grocery stores, by granting them their dreams. By 'widening' he granted them infinite reliability.
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THE MONSTER AS THE IDEAL CUSTOMER

Industry would find in the Turing machines an eternal captive market of satisfied customers. They can supply tape and ink eternally to these immortal, eternal customers who will never complain.
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THE FINANCES OF INDUSTRY BECOME SOUND

Procrustes 'widened' the capabilities of the environment of his machines to reliably settle the invoices raised by industry & business the world over.
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THE COLLECTION AGENTS ARE OUT OF BUSINESS

Industry could do without the use of horrid collection agents who would like to auction the machines for a fat commission.
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PROCRUSTES DEFINES EFFECTIVE COMPUTATION


Procrustes 'narrowed' the concept of computation to 'effective computation'.
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MODELS OF EFFECTIVE COMPUTATION

Procrustes took a leaf out of Ovid’s Metamorphoses and demonstrated, for about half a century that his multi-headed hydras of machines, can effortlessly change into many different models of effective computation.
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THE MODEL FOR EFFECTIVE COMPUTATION

Procrustes declared by 'narrowing' that the concept of 'effective computation' was identical to the capability of his machines.

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THE MONSTERS LOVE THEMSELVES


Procrustes found his machines ended up contemplating their own descriptions, and some of them got into trouble as a result of the same.
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THE MONSTER CAN REPRODUCE ITSELF


Procrustes found that some of his machines could reproduce themselves.
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THE MONSTER OF MONSTERS


Procrustes found that among his machines there was one that could simulate the behavior of any other machine. He called it a Universal Machine.

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THE MONSTER OF MONSTERS
SETS AN EXAMPLE-I


Procrustes announced by 'narrowing' that if any one had pencil, paper and the ability to simulate the Universal machine one could do all 'mathematics'.

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THE MONSTER OF MONSTERS
SETS AN EXAMPLE-II


Procrustes announced by 'narrowing' that if any one had pencil, paper and the ability to simulate the Universal machine one could do all 'computation'.

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THE MONSTER OF MONSTERS
SETS AN EXAMPLE-III


Procrustes announced by 'narrowing' that if any one had pencil, paper and the ability to simulate the Universal machine one could do all 'computation'.
By 'narrowing' one can simulate whatever mattered in the Universe.

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THE MONSTER OF MONSTERS
SETS AN EXAMPLE-IV


Procrustes announced by 'narrowing' that if any one had pencil, paper and the ability to simulate the Universal machine one could do all 'mathematics'.
The mathematicians and mathematics teachers can seemingly be shown the door.

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THE MONSTERS GET INTO A LOOP


Procrustes found that when asked to solve some problems in mathematics his machines ended up in a loop, and an eternal beating around the bush sometimes. They did not know when to stop and announce failure.
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THE MONSTERS ARE STUMPED-I


Procrustes found that when asked to solve some problems in mathematics his machines declined to volunteer.
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THE MONSTERS ARE STUMPED-II


Procrustes found that when asked to solve some problems in mathematics, the machines one by one declined to solve the same. The problem had no takers.
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THE MONSTERS ARE STUMPED - III


Procrustes wanted to know why him machines were stumped.
Why when asked to solve some problems in mathematics his machines declined to volunteer.
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THE MONSTER OF ALL MONSTERS LOVES ITSELF


Procrustes found his machines ended up contemplating their own descriptions, and some of them got into trouble as a result of the same. He used 'widening' and equipped the machines with an oracle.
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THE MONSTERS STILL LOVE THEMSELVES


Procrustes found his machines ended up contemplating their own descriptions, and some of them got into trouble as a result of the same. He used 'widening' and equipped the machines with an oracle.
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THE MONSTERS CONTINUE TO LOVE THEMSELVES


Procrustes found his new machines still ended up contemplating their own descriptions, and some of them got into trouble as a result of the same. He used 'widening' and equipped the machines with yet another oracle.
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THE MONSTERS KEEP ON LOVING THEMSELVES


Procrustes found his machines still ended up contemplating their own descriptions, and some of them got into trouble as a result of the same. He used 'widening' and equipped the machines..........
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PROCRUSTES CONSULTS ORACLE AFTER ORACLE


Procrustes then used 'widening' and equipped the machines with another oracle. He then used 'widening' and equipped the machines with yet another oracle. He then used 'widening' and equipped machines .........
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THE FINAL SOLUTION

Procrustes announced that now had his tool of mathematics to explain the Universe by simulation.

METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
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SI X BL I ND M EN AN D T HE ELEPHANT
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
ON E BL I ND M AN LE A D IN G ANOTHER
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PROCRUSTES WANTS A MEDAL


He declared it to be the greatest intellectual achievement of not only the century, but for all time throughout eternity.

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SI X BL I ND M EN AN D T HE ELEPHANT
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PROCRUSTES DECAMPS


Procrustes quietly absconded like the weavers of the Emperor's magic clothes. He left no address but took his Piggy Bank with him.
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PROCRUSTES RESURFACES


It is understood that Procrustes has surfaced again of late and is now trying new types of 'narrowing' like quantum computation.
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THE MONSTER IS CONFUSED


Needless to say using Procrustean mathematics to model and explain reality resulted in coils of undecidability springing up. Even asking Procrustean mathematics to speak up for itself resulted in coils of undecidability. This was just as in the Tower of Babel.
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THE FAMOUS PROBLEM


Oracle after oracle was desperately consulted but enigmas like the generalizations of the P=NP problem surfaced. Very few seem to understand their nature and implications clearly.
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ATTEMPTS TO SOLVE THE PROBLEM


Toil, tears and sweat for over a century were of no avail in solving the problem. This applies to numskulls like me, the hoi polloi, the glitterati and the geniuses.
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DENYING THE PROBLEM


Attempts to deny the problem as in the fable of the Fox and the Grapes does not seem to solve the problem. It keeps on surfacing everywhere.
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USING PROCRUSTEAN MATHEMATICS
FOR SIMULATION


The problem is that simulation is a very dangerous game. Procrustean mathematics can be used to specify computations to simulate the Universe.
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