GATE_1988

THEORY OF COMPUTATION

HINTS AND SOLUTIONS

Q2(viii) State the halting problem of turing machines.

It is not decidable(i.e. no algorithm exists) which can decide if an arbitary turing machine on a given input will ever halt. No halting turing machine(i.e.algorithm) exists to solve this problem.

Q2(ix) The language L={an bn |0<n<327th prime number} is a finite set and hence regular.

Q15.M2 has three copies of M.

Case(i): F2=A. In this case the first copy behaves as the same as M and the other two are don't care conditions. So the language accepted is L.

Case(ii): F2=B. In this case the second copy starts from any state and proceed to the output. So if the head of a string  reaches a final state then we accept i.e. we accept any string of L that makes an excursion to the final state..

Case (iii) In this case we accept Init(L).

Case (iv) r is not specified in the final states of M2 so we accept the empty set.

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

Go to:

2005, GATE THEORY OF COMPUTATION