Let $G_1$ be the context free grammar and $R$ be regular language. Now I have to check whether $L(G_1)=L(R)$ is decidable or not? My approach $\overline{L(G_1)}=\overline{L(R)}$. Now $L(G_1)$ not closed under complement. Therefore $L(G_1)=L(R)$ is undecidable.

Now if $G_1$ be DCFG, then $\overline{L(G_1)}=\overline{L(R)}$. Now $L(G_1)$ closed under complement because of DCFL. Therefore $L(G_1)=L(R)$ is decidable. Don't know my approach is right or not, if it wrong correct me.

  • $\begingroup$ We discourage "please check whether my answer is correct" questions, as only "yes/no" answers are possible, which won't help you or future visitors. See here and here. Can you edit your post to ask about a specific conceptual issue you're uncertain about? As a rule of thumb, a good conceptual question should be useful even to someone who isn't looking at the problem you happen to be working on. If you just need someone to check your work, you might seek out a friend, classmate, or teacher. $\endgroup$
    – D.W.
    Nov 8 '21 at 3:51

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