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Infinite-tree Automaton
In computer science and mathematical logic, an infinite-tree automaton is a state machine that deals with infinite tree structures. It can be seen as an extension of top-down finite-tree automata to infinite trees or as an extension of infinite-word automata to infinite trees. A finite automaton which runs on an infinite tree was first used by Michael Rabin for proving decidability of S2S, the monadic second-order theory with two successors. It has been further observed that tree automata and logical theories are closely connected and it allows decision problems in logic to be reduced into decision problems for automata. Definition Infinite-tree automata work on \Sigma-labeled trees. There are many slightly different definitions; here is one. A (nondeterministic) infinite-tree automaton is a tuple A = (\Sigma, D, Q, q_0, \delta, F ) with the following components. * \Sigma is an alphabet. This alphabet is used to label nodes of an input tree. * D\subset \mathbb is a finit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Tree
In computer science, a binary tree is a tree data structure in which each node has at most two children, referred to as the ''left child'' and the ''right child''. That is, it is a ''k''-ary tree with . A recursive definition using set theory is that a binary tree is a triple , where ''L'' and ''R'' are binary trees or the empty set and ''S'' is a singleton (a single–element set) containing the root. From a graph theory perspective, binary trees as defined here are arborescences. A binary tree may thus be also called a bifurcating arborescence, a term which appears in some early programming books before the modern computer science terminology prevailed. It is also possible to interpret a binary tree as an undirected, rather than directed graph, in which case a binary tree is an ordered, rooted tree. Some authors use rooted binary tree instead of ''binary tree'' to emphasize the fact that the tree is rooted, but as defined above, a binary tree is always rooted. In ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maurice Nivat
Maurice Paul Nivat (21 December 1937 – 21 September 2017) was a French computer scientist. His research in computer science spanned the areas of formal languages, programming language semantics, and discrete geometry. A 2006 citation for an honorary doctorate (Ph.D.) called Nivat one of the fathers of theoretical computer science. He was a professor at the University Paris Diderot until 2001. Early life and education Nivat was born in Clermont-Ferrand, France. His parents were high-school teachers; his father taught languages while his mother taught mathematics. His sister, Aline, became a notable mathematician. In 1954, Nivat moved with his family to Paris. Nivat was admitted to the École normale supérieure in 1956, but began working at the Blaise Pascal Institute of the French National Centre for Scientific Research, a newly established computing laboratory, in 1959. He returned to study mathematics in 1961 under the supervision of Marcel-Paul Schützenberger. His 196 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jan Van Leeuwen
Jan van Leeuwen (born 17 December 1946 in Waddinxveen) is a Dutch computer scientist and emeritus professor of computer science at the Department of Information and Computing Sciences at Utrecht University.Curriculum vitae , retrieved 2011-03-27. Education and career Van Leeuwen completed his undergraduate studies in mathematics at in 1967 and received a PhD in mathematics in 1972 from the same institution under the supervision of Dirk van Dalen.. After postdoctoral studies at the |
ω-automaton
In automata theory, a branch of theoretical computer science, an Ordinal number, ω-automaton (or stream automaton) is a variation of a finite automaton that runs on infinite, rather than finite, strings as input. Since ω-automata do not stop, they have a variety of acceptance conditions rather than simply a set of accepting states. ω-automata are useful for specifying behavior of systems that are not expected to terminate, such as hardware, operating systems and control systems. For such systems, one may want to specify a property such as "for every request, an acknowledge eventually follows", or its negation "there is a request that is not followed by an acknowledge". The former is a property of infinite words: one cannot say of a finite sequence that it satisfies this property. Classes of ω-automata include the Büchi automaton, Büchi automata, Rabin automata, Streett automata, parity automata and Muller automaton, Muller automata, each deterministic or non-deterministic. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parity Automaton
Parity may refer to: Computing * Parity bit in computing, sets the parity of data for the purpose of error detection * Parity flag in computing, indicates if the number of set bits is odd or even in the binary representation of the result of the last operation * Parity file in data processing, created in conjunction with data files and used to check data integrity and assist in data recovery Mathematics * Parity (mathematics), indicates whether a number is even or odd ** Parity of a permutation, indicates whether a permutation has an even or odd number of inversions ** Parity function, a Boolean function whose value is 1 if the input vector has an odd number of ones ** Parity learning, a problem in machine learning ** Parity of even and odd functions Other uses * Parity (physics), a symmetry property of physical quantities or processes under spatial inversion * Parity (biology), the number of times a female has given birth; gravidity and parity represent pregnancy and viability, r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Muller Automaton
In automata theory, a Muller automaton is a type of an ω-automaton. The acceptance condition separates a Muller automaton from other ω-automata. The Muller automaton is defined using a Muller acceptance condition, i.e. the set of all states visited infinitely often must be an element of the acceptance set. Both deterministic and non-deterministic Muller automata recognize the ω-regular languages. They are named after David E. Muller, an American mathematician and computer scientist, who invented them in 1963. Formal definition Formally, a deterministic Muller-automaton is a tuple ''A'' = (''Q'',Σ,δ,''q''0,F) that consists of the following information: * ''Q'' is a finite set. The elements of ''Q'' are called the ''states'' of ''A''. * Σ is a finite set called the ''alphabet'' of ''A''. * δ: ''Q'' × Σ → ''Q'' is a function, called the ''transition function'' of ''A''. * ''q''0 is an element of ''Q'', called the initial state. * F is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Streett Automaton
Streett is a surname. People with the surname * Abraham J. Streett, American politician * Harry Streett Baldwin (1894–1952), American politician * John Streett (born 1762), American colonel * Joseph M. Streett (1838–1921), American politician * St. Clair Streett (1893–1970), American general Other uses * Col. John Streett House, historic home located at Street, Harford County, Maryland, United States * Streett automaton, a class of ω-automaton that runs on infinite, rather than finite, strings See also *Street (surname) * Streat *Street A street is a public thoroughfare in a city, town or village, typically lined with Building, buildings on one or both sides. Streets often include pavements (sidewalks), pedestrian crossings, and sometimes amenities like Street light, streetligh ... * Strete {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rabin Automaton
Rabin is a Hebrew surname. It originates from the Hebrew word ''rav'' meaning Rabbi, or from the name of the specific Rabbi Abin. The most well known bearer of the name was Yitzhak Rabin, prime minister of Israel and Nobel Peace prize Laureate. People with surname Rabin * Al Rabin (1936–2012), American soap opera producer * Beatie Deutsch (née Rabin; born 1989), Haredi Jewish American-Israeli marathon runner * Chaim Menachem Rabin, German-Israeli semitic-linguist * Eve Queler (née Rabin), American conductor * Leah Rabin, wife of Yitzhak Rabin * Matthew Rabin, American professor and researcher in economics * Michael Rabin (1936–1972), American violin virtuoso * Michael O. Rabin, Israeli computer scientist and Turing Award recipient * Nathan Rabin, American film and music critic * John James Audubon (born Jean Rabin, 1785–1851), American ornithologist * Oscar Rabin (1899–1958), Latvian-born British band leader and musician * Oscar Rabin (1928–2018), Russian painte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Omega Automaton
Omega (, ; uppercase Ω, lowercase ω; Ancient Greek ὦ, later ὦ μέγα, Modern Greek ωμέγα) is the twenty-fourth and last letter in the Greek alphabet. In the Greek numeric system/isopsephy (gematria), it has a value of 800. The word literally means "great O" (''o mega'', mega meaning "great"), as opposed to omicron, which means "little O" (''o mikron'', mikron meaning "little"). In phonetic terms, the Ancient Greek Ω represented a long open-mid back rounded vowel , comparable to the "aw" of the English word ''raw'' in dialects without the cot–caught merger, in contrast to omicron, which represented the close-mid back rounded vowel , and the digraph ''ου'', which represented the long close-mid back rounded vowel . In Modern Greek, both omega and omicron represent the mid back rounded vowel or . The letter omega is transliterated into a Latin-script alphabet as ''ō'' or simply ''o''. As the final letter in the Greek alphabet, omega is often used to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
