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Let G_1 be the context free grammar. 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, it wrong correct me.