9C || C → 9C || || E → 9F || F → 9F |- || || A → .B || || C → eD || || || F → ε |- || || A → B || || C → ε || || || |} 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. Hence, the right-regular grammars generate exactly all regular languages. 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. While regular grammars can only describe regular languages, the converse is not true: regular languages can also be described by non-regular grammars. Mixing left-regular and right-regular rules If mixing of left-regular and right-regular rules is allowed, we still have a linear grammar, but not necessarily a regular one. What is more, such a grammar need not generate a regular language: all linear grammars can be easily brought into this form, and hence, such grammars can generate exactly all linear languages, including non-regular ones. For instance, the grammar G with N = {S, A}, Σ = {a, b}, P with start symbol S and rules S → aA A → Sb S → ε generates , the paradigmatic non-regular linear language. See also Regular expression, a compact notation for regular grammars Regular tree grammar, a generalization from strings to trees Prefix grammar Chomsky hierarchy , chapter III References Formal languages