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# Explain about right linear regular grammars in TOC

Regular grammar describes a regular language. It consists of four components, which are as follows −

G = (N, E, P, S)

Where,

N − finite set of non-terminal symbols,

E − a finite set of terminal symbols,

P − a set of production rules, each of one is in the forms

S → aB

S → a

S → ∈,

S ∈ N is the start symbol.

The above grammar can be of two forms −

Right Linear Regular Grammar

Left Linear Regular Grammar

## Linear Grammar

When the right side of the Grammar part has only one terminal then it's linear else non linear.

Let’s discuss about right linear grammar −

## Right linear grammar

Right linear grammar means that the non-terminal symbol will be at the right side of the production.

It is a formal grammar (N, Σ, P, S) such that all the production rules in P are of one of the following forms −

L → a, { L is a non-terminal and a is a terminal in Σ} L → aM, {L and M are non-terminals in N and a is in Σ} L → ∈.

### Example

Consider a language L= {b^{n}ab^{m}a | n>=2, m>=2}

The production rules or grammar for the given language L= {b^{n}ab^{m}a | n>=2, m>=2} is −

S→bbB ⇒for first 2 b’s B→bB|aC ⇒ any number of b’s followed by a C→bbD ⇒ 2b’s D→ bD|a ⇒ any number of b’s followed by a

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