Re: Regular grammar from CFG?

Eric Bodden <newsserver_mails@bodden.de>
7 Sep 2004 23:50:39 -0400

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From: Eric Bodden <newsserver_mails@bodden.de>
Newsgroups: comp.compilers
Date: 7 Sep 2004 23:50:39 -0400
Organization: RWTH Aachen University
References: 04-09-035
Keywords: parse, theory
Posted-Date: 07 Sep 2004 23:50:39 EDT

Hi, Lorin.


On 3 Sep 2004 12:42:40 -0400, Lorin Netsch wrote:


> Can anyone tell me how to determine if a given CFG can be represented
> as a regular grammar?


I believe there can be no way to do so, since I think, there is no way
to convert a grammar that is more than regular to one that is regular.
That is due to the Chomsky hierarchy. Type-3 grammars (regular ones)
are strictly weaker then Type-2 and so forth.


Regular grammars allow rules of the types
A -> aB
A -> a


Now just imagine the possible productions of a grammar that is not yet
regular:
- A -> B This cannot be represented by a rule of the ones above.
- A -> Ba The same.
... and so forth.


So in my eyes either a grammar is already regular or it is not. And if it
is not it will never be. Please correct me, if I am wrong.


Eric


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