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There exists a language L. We define a string w such that w∈L and w=xyz and |w| >=n for some constant integer n.What can be the maximum length of the substring xy i.e. |xy|<=?

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There exists a language L. We define a string w such that w∈L and w=xyz and |w| >=n for some constant integer n.What can be the maximum length of the substring xy i.e. |xy|<=?

(a) n

(b) |y|

(c) |x|

(d) none of the mentioned

The question was posed to me in an interview for internship.

This key question is from Pumping Lemma for Regular Language topic in portion Properties of Regular Languages of Automata Theory

1 Answer

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The correct option is (a) n

Easy explanation: It is the first conditional statement of the lemma that states that |xy|<=n, i.e. the maximum length of the substring xy in w can be n only.

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