GATE_1991

THEORY OF COMPUTATION

HINTS AND NOTES ON SOLUTIONS

Q3(xiii)ANSWER--------(A) and (C)

From an examination of the three regular expressions t contains a 0 wheras the other two do not. So L(t) cannot be a subset of the other two sets. This excludes (D).

L(r) contains 100 wheras the other two do not. So L(r) cannot be a subset of the other two. This excludes (B).

Note that (A) and (C) are the same.

Q3(xiv) ANSWER------(D)

The regular sets are the smallest class that contain all the finite sets.

Q17(a) If we take a turing machine and take away its ink it becomes a 2DFA or 2NFA. We have the standard theorem that these accept only the regular sets.

Q17(b) The nfa for the machine over {0,1} is given below:

The equivalent minimal dfa has 8 states as can be shown by constructing the dfa and minimising it. This is the example of a nfa to dfa conversion which requires an exponential number of states.

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