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


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











PREAMBLE---COMPUTATIONAL COMPLEXITY AND COMPETITIVE EXAMINATIONS--CONVERTING THE THEORY OF COMPUTATION TO A CANNIBAL

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---->
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 ....


















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







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 !





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 SOLVERS OF PROBLEMSDONOT 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 !
ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!! ANTICLIMAX!!!

(draft-----stray thoughts)**(circa 2009--)
(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)




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


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.


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.



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.


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.


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.


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.


THE RESTRICTIONS USED


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


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.


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.


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.


THE ANNOTATIONS USED


As in the ancient saying these annotations can be four score and ten in number at a time, per diagram.


CHARACTERISTICS
OF THE DIAGRAMS-I


These diagrams are basically pictorial in nature, and hence are very user friendly.


CHARACTERISTICS
OF THE DIAGRAMS-II


As they employ the principle of orthogonally they are excellent visual mnemonic diagrams.


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.


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.


THE SCOPE OF THE DIAGRAMS


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


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.


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.


ARGUMENT IV


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


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.


THE JUSTIFICATION BY PATTERN MATCHING


The intersection of small length search patterns in Google may result in a search pattern of exponential length.


THE COMPLEMENT OF A PROBLEM


A problem may be complicated to solve but its complement normally is easily demonstrated or verified.


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.


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.


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.


THE EXPRESSIVE POWER
OF
NONDETERMINISM-I


Simple descriptions can arise by employing nondeterminism.


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.


THE EXPRESSIVE POWER
OF
NONDETERMINISM-III


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


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.


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.


THE EXPRESSIVE POWER
OF
NONDETERMINISM-V


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


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.


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?


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?


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?


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.


ARGUMENT VIII


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


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.


THE IMPLEMENTATION OF CONCURRENCY-II


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


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.


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.


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.


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.


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.


THE WEAKNESS
OF WELL BEHAVED FUNCTIONS-II


This is a very general technique for all quantitative questions in all areas having competitive examinations.


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.


THE WEAKNESS
OF WELL BEHAVED FUNCTIONS-IV


In many cases the context of the question, the area of knowledge being tested, is largely irrelevant.


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.


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.


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.


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.


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.


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.


TACKLING METAMORPHOSES-III


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


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.


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.


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.


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'.



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.


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.


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).


FORMAL MODEL FOR MISREADING A QUESTION


Formally, misreading a question is the application of the operation of partial nondeterministic homomorphism or inverse homomorphism.


THE DANGERS OF MISREADING-I


Computational Complexity warns that this operation can result in a dramatic change in the complexity class.


THE DANGERS OF MISREADING-II


It can result in enforcing nondeterminism, or lead to partial undecidability or even undecidability.


THE DANGERS OF MISREADING-III


In the worst case even oracles cannot solve the problem.


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.


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.


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.


TACKLING THE EFFECTS
OF
MISREADING-II


This is different from reading the entire question carefully.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


TACKLING ALGORITHMS-X


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


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


>
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.


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.


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.


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.


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.


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.


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.


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.


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.


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'.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.



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.


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.
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.




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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.



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.


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.


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.


EPILOGUE


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



























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)