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From: graeme@aisb.ed.ac.uk (Graeme Ritchie)
Subject: Context Free Grammar Decidability
Message-ID: <Cx5JB2.E0s@aisb.ed.ac.uk>
Sender: news@aisb.ed.ac.uk (Network News Administrator)
Reply-To: graeme@aisb.ed.ac.uk (Graeme Ritchie)
Organization: Dept AI, Edinburgh University, Scotland
Date: Tue, 4 Oct 1994 14:09:01 GMT
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Xref: glinda.oz.cs.cmu.edu comp.theory:10737 comp.ai.nat-lang:2191 sci.math.symbolic:14484

Could anyone either point me at a proof, or even show me one, of the
undecidability (or otherwise) of the following, for two arbitrary
context free grammars, G1 and G2 with the same terminal alphabet V :

   Is it the case that every string in L(G1) is made up of
   a string from L(G2) with zero or more terminal symbols concatenated
   on to the front of it?
   Put another way, is L(G1) a subset of V* + L(G2),
   where  "+" indicates concatenation?

I already have the following undecidability results from the literature:

  L(G1) is regular
  L(G1) = L(G2) (even if G1 is right-linear)
  L(G1) subset of L(G2)
  L(G1) = V*
  complement of L(G1) is empty/regular/context-free
  L(G1) and L(G2) have non-empty intersection
   


All contributions gratefully received.

Graeme Ritchie                          Tel: (+44) (0)131 650 2704

Department of Artificial Intelligence
University of Edinburgh
80 South Bridge	
Edinburgh EH1 1HN                       Email: g.d.ritchie@ed.ac.uk
Scotland                                Fax: (+44) (0)131 650 6516




