Re: Regular grammar from CFG?

Ben Brosgol <brosgol@worldDOTstd.com>
8 Sep 2004 00:06:30 -0400

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From: Ben Brosgol <brosgol@worldDOTstd.com>
Newsgroups: comp.compilers
Date: 8 Sep 2004 00:06:30 -0400
Organization: The World : www.TheWorld.com : Since 1989
References: 04-09-035
Keywords: parse, theory
Posted-Date: 08 Sep 2004 00:06:30 EDT

Lorin Netsch wrote:
> Can anyone tell me how to determine if a given CFG can be represented
> as a regular grammar?
>
> If so, what method can be used to generate the right-linear grammar?


Whether an arbitrary CFG generates a regular language is undecidable.
(Theorem 4.2.2 in Seymour Ginsburg's "The Mathematical Theory of
Context-Free Languages").


The following was listed as an open problem by Ginsburg (in 1966); I'm
not sure if it's still open:


"Let G be an arbitrary [context-free] grammar. Suppose it is known that
L(G) is regular. Is it solvable to find a right-linear grammar G' such
that L(G) = L(G')?"


Ben Brosgol
brosgol at gnat.com

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