What is the difference between a context-free grammar and a regular grammar?

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What is the difference between a context-free grammar and a regular grammar?

The main difference between a context-free grammar and a regular grammar lies in the types of rules they use and the languages they can generate.

A context-free grammar (CFG) is a formal grammar where each production rule consists of a non-terminal symbol on the left-hand side and a string of terminals and/or non-terminals on the right-hand side. The rules in a CFG are not restricted by any context or surrounding symbols. CFGs are more expressive than regular grammars and can generate languages that regular grammars cannot, such as nested structures and balanced parentheses.

On the other hand, a regular grammar is a formal grammar where each production rule consists of a single terminal symbol or a non-terminal symbol followed by a single terminal symbol. The rules in a regular grammar are restricted by the context of the surrounding symbols. Regular grammars can generate regular languages, which are a subset of the languages generated by CFGs. Regular languages are characterized by their ability to be recognized by finite automata, such as deterministic or non-deterministic finite automata.

In summary, the main difference between a context-free grammar and a regular grammar is the complexity and expressiveness of the languages they can generate. CFGs are more powerful and can generate a wider range of languages, including those with nested structures, while regular grammars are more limited and can only generate regular languages.