 Solution

A DFA consists of finite $Q$, alphabet $\Sigma$, transition $\delta$, initial $q_0$, and accepting set $F$. Extend by $\hat{\delta }(q,ϵ)=q$ and $\hat{\delta }(q,wa)=\delta (\hat{\delta }(q,w),a)$. It accepts $\{w:\hat{\delta }(q_0,w)\in F\}$; a language is regular if some DFA accepts it.