1
GATE CSE 2011
+2
-0.6
Definition of the language $$L$$ with alphabet $$\left\{ a \right\}$$ is given as following. $$L = \left\{ {{a^{nk}}} \right.\left| {k > 0,\,n} \right.$$ is a positive integer constant$$\left. \, \right\}$$

What is the minimum number of states needed in a $$DFA$$ to recognize $$L$$?

A
$$k+1$$
B
$$n+1$$
C
$${2^{n + 1}}$$
D
$${2^{k + 1}}$$
2
GATE CSE 2010
+2
-0.6
Let $$L = \left\{ {w \in {{\left( {0 + 1} \right)}^ * }\left| {\,w} \right.} \right.$$ has even number of $$\,\left. {1's} \right\},$$ i.e $$L$$ is the set of all bit strings with even number of $$1's.$$ which one of rhe regular expression below represents $$L.$$
A
$$\left( {{0^ * }{{10}^ * }1} \right){}^ *$$
B
$${0^ * }\left( {{{10}^ * }{{10}^ * }} \right){}^ *$$
C
$${0^ * }\left( {{{10}^ * }1} \right){}^ * {0^ * }$$
D
$${0^ * }\,\,1\left( {{{10}^ * }1} \right){}^ * {10^ * }$$
3
GATE CSE 2010
+2
-0.6
Let $$w$$ be any string of length $$n$$ in $${\left\{ {0,1} \right\}^ * }$$. Let $$L$$ be the set of all substrings of $$w.$$ What is the minimum number of states in a non-deterministic finite automation that accepts $$L$$?
A
$$n-1$$
B
$$n$$
C
$$n+1$$
D
$${2^{n + 1}}$$
4
GATE CSE 2009
+2
-0.6
$$L = {L_1} \cap {L_2}$$ where $${L_1}$$ and $${L_2}$$ are languages defined as follows.
$${L_1} = \left\{ {{a^m}{b^m}\,c\,{a^n}{b^n}\left| {m,n \ge 0} \right.} \right\}$$
$${L_2} = \left\{ {{a^i}{b^i}{c^k}\left| {i,j,k \ge 0} \right.} \right\}$$ Then $$L$$ is
A
Not recursive
B
Regular
C
Context free but not regular
D
Recursively enumerable but not context free
GATE CSE Subjects
Theory of Computation
Operating Systems
Algorithms
Digital Logic
Database Management System
Data Structures
Computer Networks
Software Engineering
Compiler Design
Web Technologies
General Aptitude
Discrete Mathematics
Programming Languages
Computer Organization
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