1
GATE CSE 2016 Set 2
Numerical
+1
-0
The number of states in the minimum sized $$DFA$$ that accepts the language defined by the regular expression $${\left( {0 + 1} \right)^ * }\left( {0 + 1} \right){\left( {0 + 1} \right)^ * }$$\$
is ___________________.
2
GATE CSE 2016 Set 2
+1
-0.3
Language $${L_1}$$ is defined by the grammar: $$S{}_1 \to a{S_1}b|\varepsilon$$
Language $${L_2}$$ is defined by the grammar: $$S{}_2 \to ab{S_2}|\varepsilon$$

Consider the following statements:
$$P:$$ $${L_1}$$ is regular
$$Q:$$ $${L_2}$$ is regular

Which one of the following is TRUE?

A
Both $$P$$ and $$Q$$ are true
B
$$P$$ is true and $$Q$$ is false
C
$$P$$ is false and $$Q$$ is true
D
Both $$P$$ and $$Q$$ are false
3
GATE CSE 2016 Set 1
+1
-0.3
Which one of the following regular expressions represents the language: the set of all binary strings having two consecutive $$0s$$ and two consecutive $$1s?$$
A
$$\left( {0 + 1} \right){}^ * 0011\left( {0 + 1} \right){}^ * + \left( {0 + 1} \right){}^ * 1100\left( {0 + 1} \right){}^ *$$
B
$$\left( {0 + 1} \right){}^ * \left( {00\left( {0 + 1} \right){}^ * 11 + 11\left( {0 + 1} \right){}^ * \left. {00} \right)} \right.\left( {0 + 1} \right){}^ *$$
C
$$\left( {0 + 1} \right){}^ * 00\left( {0 + 1} \right){}^ * + \left( {0 + 1} \right){}^ * 11\left( {0 + 1} \right){}^ *$$
D
$$00\left( {0 + 1} \right){}^ * 11 + 11\left( {0 + 1} \right){}^ * 00$$
4
GATE CSE 2015 Set 3
+1
-0.3
Let $$L$$ be the language represented by the regular expression $$\sum {^ * 0011\sum {^ * } }$$ where $$\sum { = \left\{ {0,1} \right\}} .$$ What is the minimum number of states in a $$DFA$$ that recognizes $$\overline L$$ (complement of $$L$$)?
A
$$4$$
B
$$5$$
C
$$6$$
D
$$8$$
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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