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From: jamie@cs.sfu.ca (Jamie Andrews)
Subject: Re: Context Free Grammar Decidability
Message-ID: <1994Oct5.161057.17124@cs.sfu.ca>
Organization: Faculty of Applied Science, Simon Fraser University
References: <Cx5JB2.E0s@aisb.ed.ac.uk> <36tq3o$lbl@highway.LeidenUniv.nl>
Date: Wed, 5 Oct 1994 16:10:57 GMT
Lines: 25
Xref: glinda.oz.cs.cmu.edu comp.theory:10745 comp.ai.nat-lang:2200 sci.math.symbolic:14507

In article <36tq3o$lbl@highway.LeidenUniv.nl>,
Theo Vosse <vosse@ruls41.LeidenUniv.nl> wrote:
>Graeme Ritchie writes:
>
>|>    Put another way, is L(G1) a subset of V* + L(G2)?
>
>|> I already have the following undecidability results from the literature:
>|> ...
>|>   L(G1) subset of L(G2)
>
>Well, if G2' is a copy of G2 with the following rules added:
>
>S -> A S
>
>for each A element of V, and S is the start symbol of G2,
>then L(G2') = V* + L(G2), and the question becomes:
>is L(G1) a subset of L(G2'), which is undecidable,
>as you already mentioned.

     Yes, but the reduction goes the wrong way.  We know that
"L(G1) subset of L(G2')" is undecidable *in general*, but that
doesn't say anything about the specific cases of this problem
where L(G2') is V* + L(G2).

--J.
