GATE_1994

THEORY OF COMPUTATION

HINTS AND SOLUTIONS TO PROBLEMS

Q1.16 ANSWER (A) AND (B)

A regular grammar is trivially a context free grammar.

There are algorithms to convert nfa and nondeterministic turing machines to deterministic machines accepting the same set. For finite automata it is the subset machine. For turing machines we number the moves and generate ordered sequences of integers and map the same to the moves.

The nondeterminsitic pda is more powerful than a deterministic one. The former can accept {ai bn cn|i,n>1} U

{aj bj cm|j,m>1} but the latter cannot.

Q2.10 Answer is 0*1*

Q3.3 ANSWER----TRUE

A full adder is nothing but a finite automata. It however depends on how we encode the problem. For example the set {0n 1m 0m+n |m,n>1} is not regular.

Q19(a) ANSWER (ii)

We just run a turing machine designed to compute pi to better and better approximations. If it happens to yield a x-block of 5's we stop.

(i) is excluded as a fa cannot count.

We cannot guarentee an algorithm at present and so this excludes S.

Q19(b) ANSWER----no

Let L1 be the regular set (0+1)* and L2 any formal language(not necessaily regular). Then the union is always regular.

ANS
1987	1988	1989
1990	1991	1992
1993	1994	1995
1997	1998	1999
2000	2001	2002
2003	2004	1987
QUES
1987	1988	1989
1990	1991	1992
1993	1994	1995
1997	1998	1999
2000	2001	2002
2003	2004	1987

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2005, GATE THEORY OF COMPUTATION