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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 ...
Chomsky (1959) introduced the Chomsky hierarchy, in which context-sensitive grammars occur as "type 1" grammars; general noncontracting grammars do not occur. [2]Chomsky (1963) calls a noncontracting grammar a "type 1 grammar", and a context-sensitive grammar a "type 2 grammar", and by presenting a conversion from the former into the latter, proves the two weakly equivalent.
The complement of a context-sensitive language is itself context-sensitive [10] a result known as the Immerman–Szelepcsényi theorem. Membership of a string in a language defined by an arbitrary context-sensitive grammar, or by an arbitrary deterministic context-sensitive grammar, is a PSPACE-complete problem.
Most mildly context-sensitive grammar formalisms (in particular, LCFRS/MCFG) actually satisfy a stronger property than constant growth called semilinearity. [7] A language is semilinear if its image under the Parikh-mapping (the mapping that "forgets" the relative position of the symbols in a string, effectively treating it as a bag of words ...
Context-free languages—or rather its subset of deterministic context-free languages—are the theoretical basis for the phrase structure of most programming languages, though their syntax also includes context-sensitive name resolution due to declarations and scope.
Similarly, for context-sensitive grammars, the Penttonen normal form, also called the one-sided normal form (following Penttonen's own terminology) is: [1] [2] AB → AD or A → BC or A → a. For every context-sensitive grammar, there exists a weakly equivalent one-sided normal form. [2]
Context-sensitive language, a formal language that can be defined by a context-sensitive grammar (and equivalently by a noncontracting grammar). Context-sensitive is one of the four types of grammars in the Chomsky hierarchy; Context-sensitive help, a kind of online help that is obtained from a specific point in the state of the software ...
A growing context-sensitive language is a context-sensitive language generated by these grammars. In these grammars the "start symbol" S does not appear on the right hand side of any production rule and the length of the right hand side of each production exceeds the length of the left side, unless the left side is S. [ 1 ]