The recursive languages, which can be recognized by Turing machines that halt eventually on all inputs.Noam Chomsky called these Type 1 grammars. The context-sensitive languages, which are described by context-sensitive grammars and can be accepted by a linear bounded automaton.
Noam Chomsky called these Type 2 grammars. The context-free languages, which are described by context-free grammars and can be accepted by a ( nondeterministic) pushdown automaton.This was not a part of Chomsky's original hierarchy, but comes up in compiler design (languages in this class are used by tools such as Yacc to generate parsers) and language theory often enough to be very important. The deterministic context-free languages, which are described by a subset of the context-free grammars and can be accepted by a deterministic pushdown automaton.Noam Chomsky called these Type 3 grammars, and were part of his original hierarchy. The regular languages, which are described by left- or right- linear grammars and can be recognized by a finite automaton.The complete Chomsky hierarchy consists of the following sets of languages, described by the appropriate grammar, and accepted by the machine: These four categories of grammars describe the four categories of languages of the Chomsky hierarchy. by requiring all right hand sides to consist of a terminal followed by a nonterminal, we get the (left) regular grammars.by requiring left hand sides to consist of a single nonterminal, we get context-free grammars.by requiring the left hand side of rules to contain at most one nonterminal, we get context-sensitive grammars.arbitrary grammars can describe any language.They can also be characterized by classes of grammars defined through simple restrictions on the forms of grammar rules: They can be characterised by different types of devices used to recognise these languages: finite state automata, pushdown automata, linear bounded automata, and Turing machines, respectively. Regular languages are the smallest set context-free languages are a superset of these context-sensitive are a superset of those computable languages are again a superset. The Chomsky hierarchy is a hierarchy of classes of formal languages.
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