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Interaction Nets
Interaction nets are a graphical model of computation devised by Yves Lafont in 1990 as a generalisation of the proof structures of linear logic. An interaction net system is specified by a set of agent types and a set of interaction rules. Interaction nets are an inherently distributed model of computation in the sense that computations can take place simultaneously in many parts of an interaction net, and no synchronisation is needed. The latter is guaranteed by the strong confluence property of reduction in this model of computation. Thus interaction nets provide a natural language for massive parallelism. Interaction nets are at the heart of many implementations of the lambda calculus, such as efficient closed reduction and optimal, in Lévy's sense, Lambdascope. Definitions Interactions nets are graph-like structures consisting of ''agents'' and ''edges''. An agent of type \alpha and with ''arity'' \text(\alpha) = n \ge 0 has one ''principal port'' and n ''auxiliary ports'' ...
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Model Of Computation
In computer science, and more specifically in computability theory and computational complexity theory, a model of computation is a model which describes how an output of a mathematical function is computed given an input. A model describes how units of computations, memories, and communications are organized. The computational complexity of an algorithm can be measured given a model of computation. Using a model allows studying the performance of algorithms independently of the variations that are specific to particular implementations and specific technology. Models Models of computation can be classified into three categories: sequential models, functional models, and concurrent models. Sequential models Sequential models include: * Finite state machines * Post machines (Post–Turing machines and tag machines). * Pushdown automata * Register machines ** Random-access machines * Turing machines * Decision tree model Functional models Functional models include: * Abstract re ...
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Yves Lafont
Yves may refer to: * Yves, Charente-Maritime, a commune of the Charente-Maritime department in France * Yves (given name), including a list of people with the name * ''Yves'' (single album), a single album by Loona * ''Yves'' (film), a 2019 French film See also * Yves Tumor, U.S. musician * * Eve (other) * Evette (other) * Yvette (other) * Yvon (other) * Yvonne (other) Yvonne is a female given name. Yvonne may also refer to: * Yvonne (band), a 1993—2002 Swedish group featuring Henric de la Cour * Yvonne (cow) a German cow that escaped and was missing for several weeks in 2011 * ''Yvonne'' (musical), a 1926 We ...
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Linear Logic
Linear logic is a substructural logic proposed by Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities of the former with many of the constructive properties of the latter. Although the logic has also been studied for its own sake, more broadly, ideas from linear logic have been influential in fields such as programming languages, game semantics, and quantum physics (because linear logic can be seen as the logic of quantum information theory), as well as linguistics, particularly because of its emphasis on resource-boundedness, duality, and interaction. Linear logic lends itself to many different presentations, explanations, and intuitions. Proof-theoretically, it derives from an analysis of classical sequent calculus in which uses of (the structural rules) contraction and weakening are carefully controlled. Operationally, this means that logical deduction is no longer merely about an ever-expanding collection of persistent "truths", ...
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Lambda Calculus
Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can be used to simulate any Turing machine. It was introduced by the mathematician Alonzo Church in the 1930s as part of his research into the foundations of mathematics. Lambda calculus consists of constructing § lambda terms and performing § reduction operations on them. In the simplest form of lambda calculus, terms are built using only the following rules: * x – variable, a character or string representing a parameter or mathematical/logical value. * (\lambda x.M) – abstraction, function definition (M is a lambda term). The variable x becomes bound in the expression. * (M\ N) – application, applying a function M to an argument N. M and N are lambda terms. The reduction operations include: * (\lambda x.M \rightarrow(\l ...
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Primitives Of Interaction Nets
Primitives may refer to: * Primitive decorating, American art style * The Primitives, 1980s English alternative rock band * The Primitives, alternative country band, precursor to Uncle Tupelo * The Primitives, parody band formed in 1964 with Lou Reed and John Cale * The Primitives, British band formed in 1965 and led by Mal Ryder, active in Italy from 1965 until 1970 * ''The Primitives'', a 1962 British film directed by Alfred Travers * ''The Primitives'', a 1966 novelette by Frank Herbert * Artists of the early International Gothic period of art, in particular: ** Early Renaissance painting ** Early Netherlandish painting * Primitives (stamps), crudely designed early postage stamps * ''Primitives'' (album) by Bayonne Computing * Cryptographic primitives, low-level cryptographic algorithms frequently used to build computer security systems *Primitives (computer graphics), basic graphic elements such as lines or curves, used to create computer images See also *Primitive (disambigua ...
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Interaction Net As Configuration
Interaction is action that occurs between two or more objects, with broad use in philosophy and the sciences. It may refer to: Science * Interaction hypothesis, a theory of second language acquisition * Interaction (statistics) * Interactions of actors theory, created by cybernetician Gordon Pask * Fundamental interaction, in physics * Human–computer interaction * Social interaction between people Biology * Biological interaction * Cell–cell interaction * Drug interaction * Gene–environment interaction * Protein–protein interaction Chemistry * Aromatic interaction * Cation-pi interaction * Metallophilic interaction Arts and media * ''Interaction'' (album), 1963, by Art Farmer's Quartet * ACM ''Interactions'', a magazine published by the Association for Computing Machinery * "Interactions" (''The Spectacular Spider-Man''), an episode of the animated television series * 63rd World Science Fiction Convention, titled ''Interaction'' See also * * * Interact (disambig ...
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Interaction Rule
Interaction is action that occurs between two or more objects, with broad use in philosophy and the sciences. It may refer to: Science * Interaction hypothesis, a theory of second language acquisition * Interaction (statistics) * Interactions of actors theory, created by cybernetician Gordon Pask * Fundamental interaction, in physics * Human–computer interaction * Social interaction between people Biology * Biological interaction * Cell–cell interaction * Drug interaction * Gene–environment interaction * Protein–protein interaction Chemistry * Aromatic interaction * Cation-pi interaction * Metallophilic interaction Arts and media * ''Interaction'' (album), 1963, by Art Farmer's Quartet * ACM ''Interactions'', a magazine published by the Association for Computing Machinery * "Interactions" (''The Spectacular Spider-Man''), an episode of the animated television series * 63rd World Science Fiction Convention, titled ''Interaction'' See also * * * Interact (disambig ...
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Examples Of Interaction Nets
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) and ...
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Non-deterministic Agent
Nondeterminism or nondeterministic may refer to: Computer science *Nondeterministic programming *Nondeterministic algorithm *Nondeterministic model of computation **Nondeterministic finite automaton **Nondeterministic Turing machine *Indeterminacy in computation (other) Other *Indeterminism Indeterminism is the idea that events (or certain events, or events of certain types) are not caused, or do not cause deterministically. It is the opposite of determinism and related to chance. It is highly relevant to the philosophical probl ... (philosophy) See also * Indeterminacy (other) {{Disambiguation ...
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Graph Rewriting
In computer science, graph transformation, or graph rewriting, concerns the technique of creating a new graph out of an original graph algorithmically. It has numerous applications, ranging from software engineering (software construction and also software verification) to layout algorithms and picture generation. Graph transformations can be used as a computation abstraction. The basic idea is that if the state of a computation can be represented as a graph, further steps in that computation can then be represented as transformation rules on that graph. Such rules consist of an original graph, which is to be matched to a subgraph in the complete state, and a replacing graph, which will replace the matched subgraph. Formally, a graph rewriting system usually consists of a set of graph rewrite rules of the form L \rightarrow R, with L being called pattern graph (or left-hand side) and R being called replacement graph (or right-hand side of the rule). A graph rewrite rule is applie ...
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Lambda Calculus
Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can be used to simulate any Turing machine. It was introduced by the mathematician Alonzo Church in the 1930s as part of his research into the foundations of mathematics. Lambda calculus consists of constructing § lambda terms and performing § reduction operations on them. In the simplest form of lambda calculus, terms are built using only the following rules: * x – variable, a character or string representing a parameter or mathematical/logical value. * (\lambda x.M) – abstraction, function definition (M is a lambda term). The variable x becomes bound in the expression. * (M\ N) – application, applying a function M to an argument N. M and N are lambda terms. The reduction operations include: * (\lambda x.M \rightarrow(\l ...
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