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The Chomsky Hierarchy

The Chomsky hierarchy, as originally defined by Noam Chomsky, comprises four types of languages and their associated grammars and machines.

Language Grammar Machine Example

Regular language Regular grammar

Right-linear grammar
Left-linear grammar
Deterministic or nondeterministic finite-state acceptor a*

Context-free language Context-free grammar Nondeterministic pushdown automaton a n times b n times

Context-sensitive language Context-sensitive grammar Linear-bounded automaton a n times b n times c n times

Recursively enumerable language Unrestricted grammar Turing machine Any computable function

Language	Grammar	Machine	Example
Regular language	Regular grammar Right-linear grammar Left-linear grammar	Deterministic or nondeterministic finite-state acceptor	a*
Context-free language	Context-free grammar	Nondeterministic pushdown automaton	ab
Context-sensitive language	Context-sensitive grammar	Linear-bounded automaton	abc
Recursively enumerable language	Unrestricted grammar	Turing machine	Any computable function

These languages form a strict hierarchy; that is, regular languages is a proper subset of context-free languages context-sensitive languages recursively enumerable languages.