# Decidability of equality of CFL's

Following problem is decidable:

Given a context-free grammar $G$, is $L(G) = \varnothing$?

Following problem is undecidable:

Given a context-free grammar $G$, is $L(G) = A^{\ast}$?

Is there a characterization of context-free languages $M$ with decidable equality $L(G) = M$?

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The general equivalence problem on CFL's is undecidable, but I guess you want a subset of all CFL's for which the equivalence problem is decidable? –  sxd Aug 11 '11 at 1:10
@Dimitri: I'd like a description of the set $X$ of languages such that $M \in X$ iff it is decidable given any CFG $G$ (not neccessarily from $X$) if $L(G) = M$. –  sdcvvc Aug 11 '11 at 6:29
Crossposted to cstheory. –  sdcvvc Aug 14 '11 at 11:52