Analyzing the encoding of a DFA by a deterministic Turing machine

Asked Mar 12 '19 at 11:14

Active Mar 12 '19 at 19:07

Viewed 85 times

Define $L=\{\langle D,R \rangle \mid D$ is a DFA, $R$ is a regular expression, $L(D)=L(R) \}$

Is $L$ decidable?

Is $L$ decidable in polynomial time ($L \in P$)?

I am trying to ask: can a TM analyze a DFA encoding to output with a regular expression encoding on its tape and how fast can it be done?

edited Mar 12 '19 at 19:07

asked Mar 12 '19 at 11:14

user10364768

You can just return $D$ itself. Can you try to make your problem more precise? – Yuval Filmus Mar 12 '19 at 11:21
@YuvalFilmus thanks! I didn't realize $D$ itself works, I edited the question, please let me know if it still unclear – user10364768 Mar 12 '19 at 11:33
It’s still very imprecise. You seem to dislike DFAs, but you’re not explaining why, so it’s hard to make it more precise. – Yuval Filmus Mar 12 '19 at 11:34
@YuvalFilmus I think this edit is well-defined – user10364768 Mar 12 '19 at 11:46
Your problem is decidable. It’s a routine exercise in automata theory. – Yuval Filmus Mar 12 '19 at 11:47
What about running time? can it be done in polynomial time? I mean, is this problem in $P$? Thanks. – user10364768 Mar 12 '19 at 11:50
Deciding whether a regular expression accepts all strings is already coNP-hard. – Yuval Filmus Mar 12 '19 at 11:57
You are saying $L \in coNP-hard$? I can't see it trivially – user10364768 Mar 12 '19 at 12:11

0 Answers0