Restrictions of Regular Grammar

A regular grammar is the one where each production takes one of the following restricted forms −

B → ∧, B → w,

B → A,

B → wA.

(Where A, B are non-terminals and w is a non-empty string of terminals.)

Restrictions of regular grammar

• Only one nonterminal can appear on the right-hand side of a production.

• Nonterminal must appear on the right end of the right-hand side.

Therefore, the productions are as follows −

A → aBc and S → TU

These are not part of a regular grammar, but the production A → abcA is.

Things like A → aB|cC are allowed because they are actually two separate productions.

For any regular language, we can find a regular grammar which will produce it.

However, there may be other non-regular grammars which also produce it.

Example

For the regular language a*b*

Example

Construct a regular grammar for the language of the regular expression a*bc*

First, the strings of a*bc* start with either a or b.

S → aS | bC.

We can derive strings of the form bC, abC, aabC, and so on.

Now we need a definition for C to derive the language of c* −

C → ∧ | cC.

Therefore, a regular grammar for a *bc* can be written as follows −

S → aS | bC; C → ∧ | cC.