# Is this a regular grammar?

I went through a question asking me to categorize the following grammar.

$$S → AA, S → AB, A → a, A→BB, B → b, B → e$$

From the production rules, clearly it is Context-Free. But it accepts a finite set of strings. $\{e, a, aa, ab, abb, ba, bba, b, bb, bbb, bbbb\}$ which is regular language.

So, is the above grammar regular? Though it does not follow from the rules.

Basically my question is: Is the grammar $\{S → AA, A → a\}$ regular?.

• I got that. But according to [wikipedia][en.wikipedia.org/wiki/Regular_grammar], a regular grammar is a formal grammar that describes a regular language. Now, my grammar is describing a regular language. The set of rules are mentioned later, not as definition. – Shashwat Dec 18 '12 at 11:56