GATE 1999 PROBLEMS

THEORY OF COMPUTATION

SECTION A

Q1.4 Consider the regular expression (0+1)(0+1).....n times. The minimum state finite automaton that recognizes the language represented by this regular expression contains

(A) n states                (B) n+1 states

(C) n+2 states            (D) None of the above

Q1.5 Context-free languages are closed under:

(A) Union, intersection

(B) Union, Kleene closure

(C) Intersection, complement

(D) Complement, Kleene closure

Q1.6 Let Ld be the set of all languages accepted by a PDA by final state and Le be the set of all  languages accepted by empty stack. Which of the following is true?

(A) Ld = Le

(B) Ld is a superset of Le

(C) Ld is  a subset of Le

(D) None of the abovE

SECTION B

CS6 (a) Given that A is regular and (AUB) is regular, does it follow that B is necessarily regular? Justify your answer.

(b) Given two finite automata M1, M2 outline an algorithm to decide if L(M1) is a strict subset of L(M2).

CS7. Show that the language L = {xcx|x in {0,1}* and c is a terminal symbol} is not context free, with c not the same as o or 1.

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