Chomsky hierarchy

The Chomsky hierarchy (infrequently referred to as the Chomsky–Schützenberger hierarchy) in the fields of formal language theory, computer science, and linguistics, is a containment hierarchy of classes of formal grammars. A formal grammar describes how to form strings from a language's vocabulary (or alphabet) that are valid according to the language's syntax. Linguist Noam Chomsky theorized that four different classes of formal grammars existed that could generate increasingly complex languages. Each class can also completely generate the language of all inferior classes. The general idea of a hierarchy of grammars was first described by linguist Noam Chomsky in . Marcel-Paul Schützenberger also played a role in the development of the theory of formal languages; the paper describes the modern hierarchy including context-free grammars. Independently and alongside linguists, mathematicians were developing computation models (automata). Parsing a sentence in a language is similar to computation, and the grammars described by Chomsky proved to both resemble and be equivalent in computational power to various machine models. The following table summarizes each of Chomsky's four types of grammars, the class of language it generates, the type of automaton that recognizes it, and the form its rules must have. Note that the set of grammars corresponding to recursive languages is not a member of this hierarchy; these would be properly between Type-0 and Type-1. Every regular language is context-free, every context-free language is context-sensitive, every context-sensitive language is recursive and every recursive language is recursively enumerable. These are all proper inclusions, meaning that there exist recursively enumerable languages that are not context-sensitive, context-sensitive languages that are not context-free and context-free languages that are not regular. Regular grammar Type-3 grammars generate the regular languages.

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In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of symbols, letters, or tokens that concatenate into strings of the language. Each string concatenated from symbols of this alphabet is called a word, and the words that belong to a particular formal language are sometimes called well-formed words or well-formed formulas.

Chomsky hierarchy

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