Prove Prime' does not satisfy the Pumping Lemma

Asked Mar 17 '16 at 15:45

Active Mar 17 '16 at 15:56

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I have these two questions regarding the pumping lemma which, I do not quite fully understand. I was hoping someone can guide me through these questions.

$PRIME$ = {$a^i$ where $i$ is a prime number}

$PRIME′$ = {$a^i$ where $i$ is not prime}

A) Prove that PRIME′ is nonregular (we must first prove that PRIME is nonregular first)

B) Show that PRIME′ does satisfy the pumping lemma (that is, it can't be proven nonregular using the pumping lemma)

edited Mar 17 '16 at 15:56

asked Mar 17 '16 at 15:45

Csci319

What is $\def\P{\mathsf{PRIME}}\P$? The unary language $$ {0^p : p \in \mathbf N, p \text{ is prime}}?$$ And what is $\P'$? – martini Mar 17 '16 at 15:51
@martini just made the edits – Csci319 Mar 17 '16 at 15:56

Prove Prime' does not satisfy the Pumping Lemma

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