1
GATE CSE 1995
+2
-0.6
Which of the following definitions below generates the same language as $$L$$
Where $$L = {\left\{ x \right.^n}{y^n}\left| {n \ge \left. 1 \right\}} \right.$$
i) $$\,\,E \to xEy\left| {xy} \right.$$
ii) $$\,\,xy\left| {\left( {{x^ + }xy{y^ + }} \right)} \right.$$
iii) $${\,\,{x^ + }{y^ + }}$$
$$L = \left\{ {xn\,{y^n}\left| {n \ge 1} \right.} \right\} -$$ generates string where equal no. of $$x$$ and equal no. of $$y's.$$
$$E \to XBy\left| {xy\,abo} \right.$$ generators tips same.
A
(i) only
B
(i) and (ii)
C
(ii) and (iii)
D
(ii) only
2
GATE CSE 1994
Fill in the Blanks
+2
-0
The regular expression for the language recognized by the finite state automation of is _________.
3
GATE CSE 1994
+2
-0.6
The number of sub-strings (of all lengths inclusive) that can be formed from a character string of length $$n$$ is
A
$$n$$
B
$${n^2}$$
C
$${{n\left( {n - 1} \right)} \over 2}$$
D
$${{n\left( {n + 1} \right)} \over 2}$$
4
GATE CSE 1992
+2
-0.6
Which of the following regular expression identities are true?
A
$$r\left( {^ * } \right) = r{}^ *$$
B
$$\left( {r{}^ * s{}^ * } \right){}^ * = \left( {r + s} \right){}^ *$$
C
$$\,\left( {r + s} \right){}^ * = r{}^ * + s{}^ *$$
D
$$r{}^ * s{}^ * = r{}^ * + s{}^ *$$
GATE CSE Subjects
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