How to define a Grammar for a Language

[Steel546]

The question I'm working on has to do with defining a grammar set for a language. There is no defined set to use, it just needs to be made up.

The language is { a*b^n*c | n = 0, 1, 2, 3...}.

I understand I need the start symbol S, with vocabulary of non-terminals and terminals. I just don't understand how to get down to the a*b^n*c part. Any help understanding this would be appreciated. :)

[jhumelsine]

What you're listing looks just like the core idea for the pumping lemma from automata theory, except they use uvw instead of abc, and uvw can be sequences of any length.

Can you provide more detail? I'm not sure what you're really trying to do.

In addition to more description, can you provide some examples of what's in the language. I think it may be:

ac
abc
abbc
abbbc
abb...bbc

If that's the case, then you don't need a grammar to define this. You only need a regular expression, which is kind of what you have already, or a finite automaton to declare it.

NOTE: Regular expressions are proper subsets of BNF grammers. That is, you can always define a BNF grammar that satisfies a regular expression, but you can't reverse it the other way. Is that the crux of what you're trying to do?