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I know that the equivalence of two context-free grammars is undecidable, but what about the equivalence of a regular grammar and a context-free grammar?

Raphael
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Russell Richie
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1 Answers1

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It is undecidable whether for a given CFG $G$, $L(G)=\Delta^*$, the set of all strings (over the terminal alphabet of $G$). That answers your question, by chosing the most simple regular grammar.

Hendrik Jan
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    I thought the most simple regular language was the empty one. ;) – babou Mar 04 '15 at 01:25
  • Ah, that's excellent. Thanks, Hendrik! – Russell Richie Mar 04 '15 at 02:35
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    @babou Indeed. You made me smile. Nevertheless the concept "empty language" might be very confusing to some. In a recent exam some students noted that ${a,b,c,d}$ had $17$ subsets: $2^4$ usual ones, plus the empty set. – Hendrik Jan Mar 04 '15 at 17:18