Editing Regular grammar (section)

==Expressive power==
There is a direct one-to-one correspondence between the rules of a (strictly) right-regular grammar and those of a [[nondeterministic finite automaton]], such that the grammar generates exactly the language the automaton accepts.<ref>Hopcroft and Ullman 1979, p.218-219, Theorem 9.1 and 9.2</ref>  Hence, the right-regular grammars generate exactly all [[regular language]]s. The left-regular grammars describe the reverses of all such languages, that is, exactly the regular languages as well.

Every strict right-regular grammar is extended right-regular, while every extended right-regular grammar can be made strict by inserting new non-terminals, such that the result generates the same language; hence, extended right-regular grammars generate the regular languages as well. Analogously, so do the extended left-regular grammars.

If empty productions are disallowed, only all regular languages that do not include the empty string can be generated.<ref>Hopcroft and Ullman 1979, p.229, Exercise 9.2</ref>

While regular grammars can only describe regular languages, the [[converse (logic)|converse]] is not true: regular languages can also be described by non-regular grammars.