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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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    $\begingroup$ 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? $\endgroup$ – sxd Aug 11 '11 at 1:10
  • $\begingroup$ @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 $L(G) = M$. $\endgroup$ – sdcvvc Aug 11 '11 at 6:29
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    $\begingroup$ Crossposted to cstheory. $\endgroup$ – sdcvvc Aug 14 '11 at 11:52
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Question was answered at cstheory.

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