How can I show ithat a language is regular?

Question

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!

Answer 1

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.