Regular Language


Question 1
Consider the following two statements about regular languages:

S1: Every infinite regular language contains an undecidable language as a subset.
S2: Every finite language is regular.

Which one of the following choices is correct?
A
Only S1 is true
B
Only S2 is true
C
Both S1 and S2 are true
D
Neither S1 nor S2 is true
GATE CSE 2021 SET-2   Theory of Computation
Question 2
Let L \subseteq \{0,1\}^* be an arbitrary regular language accepted by a minimal DFA with k states. Which one of the following languages must necessarily be accepted by a minimal DFA with k states?
A
L - \{01\}
B
L \cup \{01\}
C
\{0,1\}^* -L
D
L \cdot L
GATE CSE 2021 SET-2   Theory of Computation


Question 3
Which of the following is true?
A
Every subset of a regular set is regular
B
Every finite subset of non-regular set is regular
C
The union of two non regular set is not regular
D
Infinite union of finite set is regular
ISRO CSE 2020   Theory of Computation
Question 4
Consider the following statements.

I. If L_1\cup L_2 is regular, then both L_1 \; and \; L_2 must be regular.
II. The class of regular languages is closed under infinite union.

Which of the above statements is/are TRUE?
A
I only
B
II only
C
Both I and II
D
Neither I nor II
GATE CSE 2020   Theory of Computation
Question 5
For \Sigma =\{a,b\}, let us consider the regular language
L=\{x|x=a^{2+3k} \; or \; x=b^{10+12k}, k\geq 0\}.
Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for L?
A
3
B
5
C
9
D
24
GATE CSE 2019   Theory of Computation


There are 5 questions to complete.

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