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In theoretical computer science, a context-sensitive language is a formal language that can be defined by a context-sensitive grammar (and equivalently by a noncontracting grammar). That is one of the four types of grammars in the Chomsky hierarchy. == Computational properties == Computationally, a context-sensitive language is equivalent with a linear bounded nondeterministic Turing machine, also called a linear bounded automaton. That is a non-deterministic Turing machine with a tape of only ''kn'' cells, where ''n'' is the size of the input and ''k'' is a constant associated with the machine. This means that every formal language that can be decided by such a machine is a context-sensitive language, and every context-sensitive language can be decided by such a machine. This set of languages is also known as NLINSPACE or NSPACE(''O''(''n'')), because they can be accepted using linear space on a non-deterministic Turing machine.〔.〕 The class LINSPACE (or DSPACE(''O''(''n''))) is defined the same, except using a deterministic Turing machine. Clearly LINSPACE is a subset of NLINSPACE, but it is not known whether LINSPACE=NLINSPACE.〔.〕 == Examples == One of the simplest context-sensitive, but not context-free languages is : the language of all strings consisting of ''n'' occurrences of the symbol "a", then ''n'' "b"'s, then ''n'' "c"'s (abc, aabbcc, aaabbbccc, etc.). A superset of this language, called the Bach language, is defined as the set of all strings where "a", "b" and "c" (or any other set of three symbols) occurs equally often (aabccb, baabcaccb, etc.) and is also context-sensitive.〔Bach, E. (1981). ("Discontinuous constituents in generalized categorial grammars" ). ''NELS'', vol. 11, pp. 1–12.〕〔Joshi, A.; Vijay-Shanker, K.; and Weir, D. (1991). "The convergence of mildly context-sensitive grammar formalisms". In: Sells, P., Shieber, S.M. and Wasow, T. (Editors). ''Foundational Issues in Natural Language Processing''. Cambridge MA: Bradford.〕 Another example of a context-sensitive language that is not context-free is ''L'' = . ''L'' can be shown to be a context-sensitive language by constructing a linear bounded automaton which accepts ''L''. The language can easily be shown to be neither regular nor context free by applying the respective pumping lemmas for each of the language classes to ''L''. An example of recursive language that is not context-sensitive is any recursive language whose decision is an EXPSPACE-hard problem, say, the set of pairs of equivalent regular expressions with exponentiation. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「In theoretical computer science, a context-sensitive language is a formal language that can be defined by a context-sensitive grammar (and equivalently by a noncontracting grammar). That is one of the four types of grammars in the Chomsky hierarchy.== Computational properties ==Computationally, a context-sensitive language is equivalent with a linear bounded nondeterministic Turing machine, also called a linear bounded automaton. That is a non-deterministic Turing machine with a tape of only ''kn'' cells, where ''n'' is the size of the input and ''k'' is a constant associated with the machine. This means that every formal language that can be decided by such a machine is a context-sensitive language, and every context-sensitive language can be decided by such a machine.This set of languages is also known as NLINSPACE or NSPACE(''O''(''n'')), because they can be accepted using linear space on a non-deterministic Turing machine.. The class LINSPACE (or DSPACE(''O''(''n''))) is defined the same, except using a deterministic Turing machine. Clearly LINSPACE is a subset of NLINSPACE, but it is not known whether LINSPACE=NLINSPACE..== Examples ==Bach language redirects here -->One of the simplest context-sensitive, but not context-free languages is L = \: the language of all strings consisting of ''n'' occurrences of the symbol "a", then ''n'' "b"'s, then ''n'' "c"'s (abc, aabbcc, aaabbbccc, etc.). A superset of this language, called the Bach language, is defined as the set of all strings where "a", "b" and "c" (or any other set of three symbols) occurs equally often (aabccb, baabcaccb, etc.) and is also context-sensitive.Bach, E. (1981). ("Discontinuous constituents in generalized categorial grammars" ). ''NELS'', vol. 11, pp. 1–12.Joshi, A.; Vijay-Shanker, K.; and Weir, D. (1991). "The convergence of mildly context-sensitive grammar formalisms". In: Sells, P., Shieber, S.M. and Wasow, T. (Editors). ''Foundational Issues in Natural Language Processing''. Cambridge MA: Bradford.Another example of a context-sensitive language that is not context-free is ''L'' = . ''L'' can be shown to be a context-sensitive language by constructing a linear bounded automaton which accepts ''L''. The language can easily be shown to be neither regular nor context free by applying the respective pumping lemmas for each of the language classes to ''L''.An example of recursive language that is not context-sensitive is any recursive language whose decision is an EXPSPACE-hard problem, say, the set of pairs of equivalent regular expressions with exponentiation.」の詳細全文を読む スポンサード リンク
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