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Embedded Pushdown Automata
An embedded pushdown automaton or EPDA is a computational model for parsing languages generated by tree-adjoining grammars (TAGs). It is similar to the context-free grammar-parsing pushdown automaton, but instead of using a plain stack to store symbols, it has a stack of iterated stacks that store symbols, giving TAGs a generative capacity between context-free and context-sensitive grammars, or a subset of mildly context-sensitive grammars. Embedded pushdown automata should not be confused with nested stack automata which have more computational power. History and applications EPDAs were first described by K. Vijay-Shanker in his 1988 doctoral thesis. They have since been applied to more complete descriptions of classes of mildly context-sensitive grammars and have had important roles in refining the Chomsky hierarchy. Various subgrammars, such as the linear indexed grammar, can thus be defined. While natural languages have traditionally been analyzed using context-free grammars ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Model
A computational model uses computer programs to simulate and study complex systems using an algorithmic or mechanistic approach and is widely used in a diverse range of fields spanning from physics, chemistry and biology to economics, psychology, cognitive science and computer science. The system under study is often a complex nonlinear system for which simple, intuitive analytical solutions are not readily available. Rather than deriving a mathematical analytical solution to the problem, experimentation with the model is done by adjusting the parameters of the system in the computer, and studying the differences in the outcome of the experiments. Operation theories of the model can be derived/deduced from these computational experiments. Examples of common computational models are weather forecasting models, earth simulator models, flight simulator models, molecular protein folding models, and neural network models. See also * Computational cognition *Reversible computing ... [...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 genera ... [...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. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pushdown Automaton
In the theory of computation, a branch of theoretical computer science, a pushdown automaton (PDA) is a type of automaton that employs a stack. Pushdown automata are used in theories about what can be computed by machines. They are more capable than finite-state machines but less capable than Turing machines (see below). Deterministic pushdown automata can recognize all deterministic context-free languages while nondeterministic ones can recognize all context-free languages, with the former often used in parser design. The term "pushdown" refers to the fact that the stack can be regarded as being "pushed down" like a tray dispenser at a cafeteria, since the operations never work on elements other than the top element. A stack automaton, by contrast, does allow access to and operations on deeper elements. Stack automata can recognize a strictly larger set of languages than pushdown automata. A nested stack automaton allows full access, and also allows stacked values to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stack (data Structure)
In computer science, a stack is an abstract data type that serves as a collection of elements, with two main operations: * Push, which adds an element to the collection, and * Pop, which removes the most recently added element that was not yet removed. Additionally, a peek operation can, without modifying the stack, return the value of the last element added. Calling this structure a ''stack'' is by analogy to a set of physical items stacked one atop another, such as a stack of plates. The order in which an element added to or removed from a stack is described as last in, first out, referred to by the acronym LIFO. As with a stack of physical objects, this structure makes it easy to take an item off the top of the stack, but accessing a datum deeper in the stack may require taking off multiple other items first. Considered as a linear data structure, or more abstractly a sequential collection, the push and pop operations occur only at one end of the structure, referred to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Context-sensitive Grammar
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 CSG but not by context-free grammars. Context-sensitive grammars are less general (in the same sense) than unrestricted grammars. Thus, CSG are positioned between context-free and unrestricted grammars in the Chomsky hierarchy. A formal language that can be described by a context-sensitive grammar, or, equivalently, by a noncontracting grammar or a linear bounded automaton, is called a context-sensitive language. Some textbooks actually define CSGs as non-contracting, although this is not how Noam Chomsky defined them in 1959. This choice of definition makes no difference in terms of the languages generated (i.e. the two definitions are weakly equivalent), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mildly Context-sensitive Grammar
In computational linguistics, the term mildly context-sensitive grammar formalisms refers to several grammar formalisms that have been developed in an effort to provide adequate descriptions of the syntactic structure of 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 Netherlands, 1984.Stuart M. Shieber.Evidenc ... [...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] |
University Of Pennsylvania
The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universities by numerous organizations and scholars. While the university dates its founding to 1740, it was created by Benjamin Franklin and other Philadelphia citizens in 1749. It is a member of the Ivy League. The university has four undergraduate schools as well as twelve graduate and professional schools. Schools enrolling undergraduates include the College of Arts and Sciences, the School of Engineering and Applied Science, the Wharton School, and the School of Nursing. Among its highly ranked graduate schools are its law school, whose first professor wrote the first draft of the United States Constitution, its medical school, the first in North America, and Wharton, the first collegiate business school. Penn's endowment is US$20.7 billio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chomsky Hierarchy
In formal language theory, computer science and linguistics, the Chomsky hierarchy (also referred to as the Chomsky–Schützenberger hierarchy) is a containment hierarchy of classes of formal grammars. This hierarchy of grammars was described by Noam Chomsky in 1956. It is also named after Marcel-Paul Schützenberger, who played a crucial role in the development of the theory of formal languages. Formal grammars A formal grammar of this type consists of a finite set of '' production rules'' (''left-hand side'' → ''right-hand side''), where each side consists of a finite sequence of the following symbols: * a finite set of ''nonterminal symbols'' (indicating that some production rule can yet be applied) * a finite set of ''terminal symbols'' (indicating that no production rule can be applied) * a ''start symbol'' (a distinguished nonterminal symbol) A formal grammar provides an axiom schema for (or ''generates'') a ''formal language'', which is a (usually infinite) s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, nonterminal symbols, * ''T'' is a set ("alphabet (formal languages), alphabet") of terminal symbols, * ''F'' is a set of so-called ''index symbols'', or ''indices'', * ''S'' ∈ ''N'' is the ''start symbol (formal languages), start symbol'', and * ''P'' is a finite set of ''Production (formal languages), productions''. In productions as well as in derivations of indexed grammars, a string ("stack") ''σ'' ∈ ''F''Kleene star, * of index symbols is attached to every nonterminal symbol ''A'' ∈ ''N'', de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transformational-generative Grammar
In linguistics, transformational grammar (TG) or transformational-generative grammar (TGG) is part of the theory of generative grammar, especially of natural languages. It considers grammar to be a system of rules that generate exactly those combinations of words that form grammatical sentences in a given language and involves the use of defined operations (called transformations) to produce new sentences from existing ones. The method is commonly associated with American linguist Noam Chomsky. Generative algebra was first introduced to general linguistics by the structural linguist Louis Hjelmslev although the method was described before him by Albert Sechehaye in 1908. Chomsky adopted the concept of transformations from his teacher Zellig Harris, who followed the American descriptivist separation of semantics from syntax. Hjelmslev's structuralist conception including semantics and pragmatics is incorporated into functional grammar. Historical context Transformational analys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
