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Prove that {anbamba2m+n:n,m≥1} is not regular using pumping lemma

Prove that {anbamba2m+n:n,m≥1} is not regular using pumping lemma

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Expert Solution

To prove that is not regular, use the pumping lemma for regular languages as follows.

Let the pumping length be . Consider the word which has length at least p, which is in the language as per the definition of the language with .

Consider any breakup of the word . Then xy must consist of only 'a's from the first block, otherwise it's length will exceed p. Hence . Now consider the pumped down word . Then this word has , but the number of 'a's in the last block is . As , this means , hence . This means that the word w' doesn't satisfy the property to be in the language, hence .

This proves the language is not regular using the pumping lemma for regular language. Comment in case of any doubts.

venereology answered 1 year ago
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