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Range Concatenation Grammar
Range concatenation grammar (RCG) is a grammar formalism developed by Pierre Boullier in 1998 as an attempt to characterize a number of phenomena of natural language, such as Chinese numbers and German word order scrambling, which are outside the bounds of the mildly context-sensitive languages. From a theoretical point of view, any language that can be parsed in polynomial time belongs to the subset of RCG called positive range concatenation grammars, and reciprocally. Though intended as a variant on Groenink's literal movement grammar In linguistics and theoretical computer science, literal movement grammars (LMGs) are a grammar formalism intended to characterize certain extraposition phenomena of natural language such as topicalization and cross-serial dependency. LMGs extend t ...s (LMGs), RCGs treat the grammatical process more as a proof than as a production. Whereas LMGs produce a terminal string from a start predicate, RCGs aim to reduce a start predicate (which predicate ...
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Mildly Context-sensitive Language
In computational linguistics, the term mildly context-sensitive grammar formalisms refers to several grammar formalisms that have been developed in an effort to provide linguistic description, adequate descriptions of the syntactic structure of language, natural language. Every mildly context-sensitive grammar formalism defines a class of mildly context-sensitive grammars (the grammars that can be specified in the formalism), and therefore also a class of mildly context-sensitive languages (the formal languages generated by the grammars). Background By 1985, several researchers in descriptive and mathematical linguistics had provided evidence against the hypothesis that the syntactic structure of natural language can be adequately described by context-free grammars.Riny Huybregts. "The Weak Inadequacy of Context-Free Phrase Structure Grammars". In Ger de Haan, Mieke Trommelen, and Wim Zonneveld, editors, ''Van periferie naar kern'', pages 81–99. Foris, Dordrecht, The Netherland ...
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PTIME
In computational complexity theory, P, also known as PTIME or DTIME(''n''O(1)), is a fundamental complexity class. It contains all decision problems that can be solved by a deterministic Turing machine using a polynomial amount of computation time, or polynomial time. Cobham's thesis holds that P is the class of computational problems that are "efficiently solvable" or " tractable". This is inexact: in practice, some problems not known to be in P have practical solutions, and some that are in P do not, but this is a useful rule of thumb. Definition A language ''L'' is in P if and only if there exists a deterministic Turing machine ''M'', such that * ''M'' runs for polynomial time on all inputs * For all ''x'' in ''L'', ''M'' outputs 1 * For all ''x'' not in ''L'', ''M'' outputs 0 P can also be viewed as a uniform family of boolean circuits. A language ''L'' is in P if and only if there exists a polynomial-time uniform family of boolean circuits \, such that * For all n \in ...
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Literal Movement Grammar
In linguistics and theoretical computer science, literal movement grammars (LMGs) are a grammar formalism intended to characterize certain extraposition phenomena of natural language such as topicalization and cross-serial dependency. LMGs extend the class of context free grammars (CFGs) by adding introducing pattern-matched function-like rewrite semantics, as well as the operations of variable binding and slash deletion. LMGs were introduced by A.V. Groenink in 1995.Groenink, Annius V. 1995. Literal Movement Grammars. In ''Proceedings of the 7th EACL Conference''. Description The basic rewrite operation of an LMG is very similar to that of a CFG, with the addition of arguments to the non-terminal symbols. Where a context-free rewrite rule obeys the general schema S \to \alpha for some non-terminal S and some string of terminals and/or non-terminals \alpha, an LMG rewrite rule obeys the general schema X(x_1, ..., x_n) \to \alpha, where X is a non-terminal with arity n (called ...
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Formal Languages
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''. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar, which consists of its formation rules. In computer science, formal languages are used among others as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages in which the words of the language represent concepts that are associated with particular meanings or semantics. In computational complex ...
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