How to use DFA/NFA to prove the language {$0^n 1^$ | x ∈ Σ*, n ≥ 1} is regular? I'm trying to prove the language L = {$0^n 1^$ | x ∈ Σ*, n ≥ 1} is regular, but don't know how to present it in a DFA/NFA.
I'm thinking to have n+1 states in a NFA, with the start state as the accepting state. The NFA reada $0$s to go from q$0$ to q$n+1$, then reading $1$s or $0$s to stay in the q$n+1$, then reading the same number of $1$s to go back to the q$0$. Is this a valid way to prove L is regular?
Your language consists of all words starting with $0$ and ending with $1$.