Explain the concept of a regular grammar.

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Explain the concept of a regular grammar.

A regular grammar is a type of formal grammar that generates regular languages. It consists of a set of production rules, where each rule has the form A -> w, where A is a non-terminal symbol and w is a string of terminal and/or non-terminal symbols. The production rules in a regular grammar are restricted to three types:

1. A -> aB or A -> a: This type of rule allows the non-terminal symbol A to be replaced by a terminal symbol a followed by a non-terminal symbol B, or simply by a terminal symbol a.

2. A -> ε: This type of rule allows the non-terminal symbol A to be replaced by the empty string ε.

3. A -> εB: This type of rule allows the non-terminal symbol A to be replaced by the empty string ε followed by a non-terminal symbol B.

Regular grammars are closely related to regular expressions and finite automata. They can be used to describe regular languages, which are languages that can be recognized by finite automata. Regular grammars are less expressive than other types of grammars, such as context-free grammars, as they cannot generate languages with nested structures or non-regular properties.