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Linear-indexed Grammar
Indexed grammars are a generalization of context-free grammars in that nonterminals are equipped with lists of ''flags'', or ''index symbols''. The language produced by an indexed grammar is called an indexed language. Definition Modern definition by Hopcroft and Ullman In contemporary publications following Hopcroft and Ullman (1979), an indexed grammar is formally defined a 5-tuple ''G'' = ⟨''N'',''T'',''F'',''P'',''S''⟩ where * ''N'' is a set of variables or nonterminal symbols, * ''T'' is a set ("alphabet") of terminal symbols, * ''F'' is a set of so-called ''index symbols'', or ''indices'', * ''S'' ∈ ''N'' is the '' start symbol'', and * ''P'' is a finite set of '' productions''. In productions as well as in derivations of indexed grammars, a string ("stack") ''σ'' ∈ ''F'' * of index symbols is attached to every nonterminal symbol ''A'' ∈ ''N'', denoted by ''A'' 'σ''" and " are meta symbols to indicate the stack. Terminal symbols may not be followed by index ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Context-free Grammar
In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules are of the form :A\ \to\ \alpha with A a ''single'' nonterminal symbol, and \alpha a string of terminals and/or nonterminals (\alpha can be empty). A formal grammar is "context-free" if its production rules can be applied regardless of the context of a nonterminal. No matter which symbols surround it, the single nonterminal on the left hand side can always be replaced by the right hand side. This is what distinguishes it from a context-sensitive grammar. A formal grammar is essentially a set of production rules that describe all possible strings in a given formal language. Production rules are simple replacements. For example, the first rule in the picture, :\langle\text\rangle \to \langle\text\rangle = \langle\text\rangle ; replaces \langle\text\rangle with \langle\text\rangle = \langle\text\rangle ;. There can be multiple replacement rules for a given nonterminal symbol. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nested Stack Automata
In automata theory, a nested stack automaton is a finite automaton that can make use of a stack containing data which can be additional stacks. Like a stack automaton, a nested stack automaton may step up or down in the stack, and read the current symbol; in addition, it may at any place create a new stack, operate on that one, eventually destroy it, and continue operating on the old stack. This way, stacks can be nested recursively to an arbitrary depth; however, the automaton always operates on the innermost stack only. A nested stack automaton is capable of recognizing an indexed language Indexed languages are a class of formal languages discovered by Alfred Aho; they are described by indexed grammars and can be recognized by nested stack automata. Indexed languages are a proper subset of context-sensitive languages. They qualify as ..., and in fact the class of indexed languages is exactly the class of languages accepted by one-way nondeterministic nested stack automata. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LCFRS
Generalized context-free grammar (GCFG) is a grammar formalism that expands on context-free grammars by adding potentially non-context-free composition functions to rewrite rules. Head grammar (and its weak equivalents) is an instance of such a GCFG which is known to be especially adept at handling a wide variety of non-CF properties of natural language. Description A GCFG consists of two components: a set of composition functions that combine string tuples, and a set of rewrite rules. The composition functions all have the form f(\langle x_1, ..., x_m \rangle, \langle y_1, ..., y_n \rangle, ...) = \gamma, where \gamma is either a single string tuple, or some use of a (potentially different) composition function which reduces to a string tuple. Rewrite rules look like X \to f(Y, Z, ...), where Y, Z, ... are string tuples or non-terminal symbols. The rewrite semantics of GCFGs is fairly straightforward. An occurrence of a non-terminal symbol is rewritten using rewrite rules as in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivalence (formal Languages)
In formal language theory, weak equivalence of two grammars means they generate the same set of strings, i.e. that the formal language they generate is the same. In compiler theory the notion is distinguished from strong (or structural) equivalence, which additionally means that the two parse trees are reasonably similar in that the same semantic interpretation can be assigned to both. Vijay-Shanker and Weir (1994) demonstrates that Linear Indexed Grammars, Combinatory Categorial Grammars, Tree-adjoining Grammars, and Head Grammars are weakly equivalent formalisms, in that they all define the same string languages. On the other hand, if two grammars generate the same set of derivation trees (or more generally, the same set of abstract syntactic objects), then the two grammars are strongly equivalent. Chomsky (1963) introduces the notion of strong equivalence, and argues that only strong equivalence is relevant when comparing grammar formalisms. Kornai and Pullum (1990)Kornai, A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Indexed Grammars
Linearity is the property of a mathematical relationship (''function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear relationship of voltage and current in an electrical conductor ( Ohm's law), and the relationship of mass and weight. By contrast, more complicated relationships are ''nonlinear''. Generalized for functions in more than one dimension, linearity means the property of a function of being compatible with addition and scaling, also known as the superposition principle. The word linear comes from Latin ''linearis'', "pertaining to or resembling a line". In mathematics In mathematics, a linear map or linear function ''f''(''x'') is a function that satisfies the two properties: * Additivity: . * Homogeneity of degree 1: for all α. These properties are known as the superposition principle. In this definition, ''x'' is not necessarily a rea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Head Grammar
Head grammar (HG) is a grammar formalism introduced in Carl Pollard (1984) Pollard, C. 1984. ''Generalized Phrase Structure Grammars, Head Grammars, and Natural Language''. Ph.D. thesis, Stanford University, CA. as an extension of the context-free grammar class of grammars. Head grammar is therefore a type of phrase structure grammar, as opposed to a dependency grammar. The class of head grammars is a subset of the linear context-free rewriting systems. One typical way of defining head grammars is to replace the terminal strings of CFGs with indexed terminal strings, where the index denotes the "head" word of the string. Thus, for example, a CF rule such as A \to abc might instead be A \to (abc, 0), where the 0th terminal, the ''a'', is the head of the resulting terminal string. For convenience of notation, such a rule could be written as just the terminal string, with the head terminal denoted by some sort of mark, as in A \to \widehatbc. Two fundamental operations are then ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tree-adjoining Grammar
Tree-adjoining grammar (TAG) is a grammar formalism defined by Aravind Joshi. Tree-adjoining grammars are somewhat similar to context-free grammars, but the elementary unit of rewriting is the tree rather than the symbol. Whereas context-free grammars have rules for rewriting symbols as strings of other symbols, tree-adjoining grammars have rules for rewriting the nodes of trees as other trees (see tree (graph theory) and tree (data structure)). History TAG originated in investigations by Joshi and his students into the family of adjunction grammars (AG), the "string grammar" of Zellig Harris. AGs handle exocentric properties of language in a natural and effective way, but do not have a good characterization of endocentric constructions; the converse is true of rewrite grammars, or phrase-structure grammar (PSG). In 1969, Joshi introduced a family of grammars that exploits this complementarity by mixing the two types of rules. A few very simple rewrite rules suffice to gen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatory Categorial Grammar
Combinatory categorial grammar (CCG) is an efficiently parsable, yet linguistically expressive grammar formalism. It has a transparent interface between surface syntax and underlying semantic representation, including predicate–argument structure, quantification and information structure. The formalism generates constituency-based structures (as opposed to dependency-based ones) and is therefore a type of phrase structure grammar (as opposed to a dependency grammar). CCG relies on combinatory logic, which has the same expressive power as the lambda calculus, but builds its expressions differently. The first linguistic and psycholinguistic arguments for basing the grammar on combinators were put forth by Steedman and Szabolcsi. More recent prominent proponents of the approach are Pauline Jacobson anJason Baldridge In these new approaches, the combinator B (the compositor) is useful in creating long-distance dependencies, as in "Who do you think Mary is talking about?" and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Examples
Example may refer to: * '' exempli gratia'' (e.g.), usually read out in English as "for example" * .example, reserved as a domain name that may not be installed as a top-level domain of the Internet ** example.com, example.net, example.org, example.edu, second-level domain names reserved for use in documentation as examples * HMS ''Example'' (P165), an Archer-class patrol and training vessel of the Royal Navy Arts * ''The Example'', a 1634 play by James Shirley * ''The Example'' (comics), a 2009 graphic novel by Tom Taylor and Colin Wilson * Example (musician), the British dance musician Elliot John Gleave (born 1982) * ''Example'' (album), a 1995 album by American rock band For Squirrels See also * * Exemplar (other), a prototype or model which others can use to understand a topic better * Exemplum, medieval collections of short stories to be told in sermons * Eixample The Eixample (; ) is a district of Barcelona between the old city ( Ciutat Vella) an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modern Definition By Hopcroft And Ullman
Modern may refer to: History * Modern history ** Early Modern period ** Late Modern period *** 18th century *** 19th century *** 20th century ** Contemporary history * Moderns, a faction of Freemasonry that existed in the 18th century Philosophy and sociology * Modernity, a loosely defined concept delineating a number of societal, economic and ideological features that contrast with "pre-modern" times or societies ** Late modernity Art * Modernism ** Modernist poetry * Modern art, a form of art * Modern dance, a dance form developed in the early 20th century * Modern architecture, a broad movement and period in architectural history * Modern music (other) Geography *Modra, a Slovak city, referred to in the German language as "Modern" Typography * Modern (typeface), a raster font packaged with Windows XP * Another name for the typeface classification known as Didone (typography) * Modern, a generic font family name for fixed-pitch serif and sans serif fonts ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gerald Gazdar
Gerald James Michael Gazdar, FBA (born 24 February 1950) is a British linguist and computer scientist. Education He was educated at Heath Mount School, Bradfield College, the University of East Anglia (BA, 1970) and the University of Reading (MA, PhD). Career and research Gazdar was appointed a lecturer at the University of Sussex in 1975, and became Professor of Computational Linguistics there in 1985. He retired in 2002. Gazdar defined Linear Indexed Grammars and pioneered, along with his colleagues Ewan Klein, Geoffrey Pullum Geoffrey Keith Pullum (; born 8 March 1945) is a British and American linguist specialising in the study of English. He is Professor Emeritus of General Linguistics at the University of Edinburgh. Pullum is a co-author of ''The Cambridge Gram ... and Ivan Sag, the framework of Generalized Phrase Structure Grammars. References 1950 births Living people People educated at Heath Mount School People educated at Bradfield College Alum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
