Re: Regular grammar from CFG?

"Eric Bodden" <newsserver_mails@bodden.de> schrieb


> 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


This is not quite correct. Take a look at the definitions of left linear,
right linear, strongly left linear and strongly right linear grammars


>
> 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.


But this is a so called unit production which can be easily removed from
any grammar without changing the generated language.


> - A -> Ba The same.


In a left linear grammar productions like this are allowed and yet left
linear grammars generate regular languages


> ... 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.

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