I have a very quick question about regular languages, I think $\{a^{2n}| n\geq 1\}$ is regular. I do know that pumping lemma can be used to show something that is not regular. I am wondering what should I use in order to show that $\{a^{2n}| n\geq 1\}$ is regular.

Thanks ahead!

  • $\begingroup$ I'd suggest you to also add a tag for regular languages :) $\endgroup$
    – frabala
    Feb 28 '14 at 5:11

You can show that a language, $L$, is regular with one of those:

  • Express the language with a regex
  • Make an NFA that recognizes $L$
  • Make a DFA that recognizes $L$
  • Determine a primitive recursive function $f:\Sigma^*\to\{0,1\}$with the property $$f(x)=\begin{cases}1\text{, if } x\in L \\0\text{, else}\end{cases}$$ where $\Sigma$ is the alphabet of the language.

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