GATE CS 2014 Set 1 — Question 25
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Theory of Computation → Finite Automata & Regular Languages
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Question
Which one of the following is TRUE?
Correct answer
(C) The language L = \w w has 3k+1 b's for some k ∈ N with Σ = \a, b\\ is regular.
Solution
Let's analyze each option:(A) is a classic Context-Free Language (CFL) but is not regular. A finite automaton cannot count the number of 's to match with 's for arbitrary .(B) is not regular. This can be proven using the Pumping Lemma.(C) means the number of 's is congruent to . This requires counting modulo 3, which can be done with a finite automaton (DFA) having 3 states (representing remainders 0, 1, 2). Since a DFA can be constructed, the language is regular.(D) is a Context-Sensitive Language (CSL) but not regular (and not even Context-Free). It requires checking if the first half of the string is identical to the second half.Therefore, option (C) is the correct statement.
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