GATE CS 2019 Set 1 — Question 25
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Theory of Computation → Finite Automata & Regular Languages → Pumping Lemma (Regular)
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Question
For , let us consider the regular language . Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for ?
Correct answer
(D) 24
Solution
A number is a pumping length for if every string with can be written as with , and for all .The strings of are (lengths ) and (lengths ). cannot be pumped at all. Any with gives , and no -string shorter than 10 is in . So a pumping length must satisfy , which rules out (A) 3, (B) 5 and (C) 9. works.
- with length : take , . Then and for all (since ).
- with length (so ): take , . Then and for all .
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