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From: tromp@math.uwaterloo.ca (John Tromp)
Subject: Re: Context Free Grammar Decidability
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Date: Wed, 5 Oct 1994 13:55:52 GMT
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In article <36tq3o$lbl@highway.LeidenUniv.nl>, vosse@ruls41.LeidenUniv.nl (Theo Vosse) writes:
> Graeme Ritchie writes:

Question Q:
-----------
> |>    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.

However, this doesn't prove that question Q is undecidable.
To show that, you'd need to give a reduction *from* a known
undecidable question *to* question Q.
Also, note that by equiping G2 with a special structure, as you did,
you may have rendered the question "is L(G1) a subset of L(G2')?"
decidable, even though for arbitrary G2', it is undecidable.

regards,

%!PS			     %  -John Tromp (tromp@math.uwaterloo.ca)
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