GATE 1992 PROBLEMS

THEORY OF COMPUTATION

PART A

Q2(xii) Which of the following regular expression identities are true?

(A) r(*) = r*

(B) (r*S*)* = (r + s)*

(C) (r + s)* = r* + s*

(D) r*s* = r* + s*

Q2(xviii) If G is a context-free grammar and w is a string of length l in L(G), how long is a derivation of w in G, if G is in the Chomky normal form?

(A)  2l       (B) 2l + 1     (C) 2l - 1         (D) l

Q2(xix) Context-free languages are

(A) closed under union                                        (B) closed under complementation

(C) closed under intersection                                (D) closed under Kleene closure

Q2(xx) In which of the cases stated below is the following statement true?

"For every nondeterministic machine M1 there exists an equivalent deterministic machine M2 recognizing the same language".

(A) M1 in a nondeterministic finite automaton.

(B) M1 is a nondeterministic PDA

(C) M1 is a nondeterministic Turing machine

(D) For no machine M1 is the above statement True

PART B

Q16 Which of the following three statements are true? Prove your answer.

(i) The union of two recursive languages is recursive.

(ii) The language {0^n | n is a prime } is not regular.

(iii) Regular languages are closed under infinite union.

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