Chomsky hierarchy in the context of "Automata theory"

Avram Noam Chomsky (born December 7, 1928) is an American professor and public intellectual known for his work in linguistics, political activism, and social criticism. Sometimes called "the father of modern linguistics", Chomsky is also a major figure in analytic philosophy and one of the founders of the field of cognitive science. He is a laureate professor of linguistics at the University of Arizona and an institute professor emeritus at the Massachusetts Institute of Technology (MIT). Among the most cited living authors, Chomsky has written more than 150 books on topics such as linguistics, war, and politics. In addition to his work in linguistics, since the 1960s Chomsky has been an influential voice on the American left as a consistent critic of U.S. foreign policy, contemporary capitalism, and corporate influence on political institutions and the media.

Born to Ashkenazi Jewish immigrants in Philadelphia, Chomsky developed an early interest in anarchism from alternative bookstores in New York City. He studied at the University of Pennsylvania. During his postgraduate work in the Harvard Society of Fellows, Chomsky developed the theory of transformational grammar for which he earned his doctorate in 1955. That year he began teaching at MIT, and in 1957 emerged as a significant figure in linguistics with his landmark work Syntactic Structures, which played a major role in remodeling the study of language. From 1958 to 1959 Chomsky was a National Science Foundation fellow at the Institute for Advanced Study. He created or co-created the universal grammar theory, the generative grammar theory, the Chomsky hierarchy, and the minimalist program. Chomsky also played a pivotal role in the decline of linguistic behaviorism, and was particularly critical of the work of B. F. Skinner.

The term phrase structure grammar was originally introduced by Noam Chomsky as the term for grammar studied previously by Emil Post and Axel Thue (Post canonical systems). Some authors, however, reserve the term for more restricted grammars in the Chomsky hierarchy: context-sensitive grammars or context-free grammars. In a broader sense, phrase structure grammars are also known as constituency grammars. The defining character of phrase structure grammars is thus their adherence to the constituency relation, as opposed to the dependency relation of dependency grammars.

In theoretical computer science and formal language theory, a regular language (also called a rational language) is a formal language that can be defined by a regular expression, in the strict sense in theoretical computer science (as opposed to many modern regular expression engines, which are augmented with features that allow the recognition of non-regular languages).

Alternatively, a regular language can be defined as a language recognised by a finite automaton. The equivalence of regular expressions and finite automata is known as Kleene's theorem (after American mathematician Stephen Cole Kleene). In the Chomsky hierarchy, regular languages are the languages generated by Type-3 grammars.

A context-sensitive grammar (CSG) is a formal grammar in which the left-hand sides and right-hand sides of any production rules may be surrounded by a context of terminal and nonterminal symbols. Context-sensitive grammars are more general than context-free grammars, in the sense that there are languages that can be described by a CSG but not by a context-free grammar. Context-sensitive grammars are less general (in the same sense) than unrestricted grammars. Thus, CSGs are positioned between context-free and unrestricted grammars in the Chomsky hierarchy.

A formal language that can be described by a context-sensitive grammar, or, equivalently, by a noncontracting grammar or a linear bounded automaton, is called a context-sensitive language. Some textbooks actually define CSGs as non-contracting, although this is not how Noam Chomsky defined them in 1959. This choice of definition makes no difference in terms of the languages generated (i.e. the two definitions are weakly equivalent), but it does make a difference in terms of what grammars are structurally considered context-sensitive; the latter issue was analyzed by Chomsky in 1963.