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Parity Game
A parity game is played on a colored directed graph, where each node has been colored by a priority – one of (usually) finitely many natural numbers. Two players, 0 and 1, move a (single, shared) token along the edges of the graph. The owner of the node that the token falls on selects the successor node (does the next move). The players keep moving the token, resulting in a (possibly infinite) path, called a play. The winner of a finite play is the player whose opponent is unable to move. The winner of an infinite play is determined by the priorities appearing in the play. Typically, player 0 wins an infinite play if the largest priority that occurs infinitely often in the play is even. Player 1 wins otherwise. This explains the word "parity" in the title. Parity games lie in the third level of the Borel hierarchy, and are consequently determined. Games related to parity games were implicitly used in Rabin's proof of decidability of the monadic second-order theory of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Example Parity Game Solved
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, and 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) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
P (complexity)
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory Game Classes
A game is a structured type of play usually undertaken for entertainment or fun, and sometimes used as an educational tool. Many games are also considered to be work (such as professional players of spectator sports or video games) or art (such as games involving an artistic layout such as mahjong, solitaire, or some video games). Games have a wide range of occasions, reflecting both the generality of its concept and the variety of its play. Games are sometimes played purely for enjoyment, sometimes for achievement or reward as well. They can be played alone, in teams, or online; by amateurs or by professionals. The players may have an audience of non-players, such as when people are entertained by watching a chess championship. On the other hand, players in a game may constitute their own audience as they take their turn to play. Often, part of the entertainment for children playing a game is deciding who is part of their audience and who participates as a player. A toy and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moshe Y
Moshe is the Hebrew version of the masculine given name Moses. Bearers include: * Moshe Arens (1925–2019), Israeli politician * Moshe Bar, several people * Moshe Bejski (1921–2007), Israeli judge * Moshe Brener (born 1971), Israeli basketball player * Moshe Czerniak (1910–1984), Israeli chess master * Moshe Dayan (1915–1981), Israeli military leader and politician * Moshe Erem (1896–1978), Israeli politician * Moshe Feinstein (1895–1986), Russian-born American Orthodox Jewish rabbi, scholar, and posek * Moshe Gil (1921–2014), Israeli historian * Moshe Gutnick, Australian Orthodox Chabad rabbi * Moshe Hirsch (1929–2010), Jewish activist and Palestinian politician * Moshe Ivgy (born 1953), Israeli actor * Moshe Jarden (born 1942), Israeli mathematician * Moshe Kahlon (born 1960) Israeli politician * Moshe Kasher (born 1979), American comedian * Moshe Katsav (born 1945), Israeli-Iranian president of Israel * Moshe Katz, several people * Moshe Kaveh (born 1943 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joel Spencer
Joel Spencer (born April 20, 1946) is an American mathematician. He is a combinatorialist who has worked on probabilistic methods in combinatorics and on Ramsey theory. He received his doctorate from Harvard University in 1970, under the supervision of Andrew Gleason. He is currently () a professor at the Courant Institute of Mathematical Sciences of New York University. Spencer's work was heavily influenced by Paul Erdős, with whom he coauthored many papers (giving him an Erdős number of 1). In 1963, while studying at the Massachusetts Institute of Technology, Spencer became a Putnam Fellow. In 1984, Spencer received a Lester R. Ford Award. He was an Erdős Lecturer at Hebrew University of Jerusalem in 2001. In 2012, he became a fellow of the American Mathematical Society. He was elected as a fellow of the Society for Industrial and Applied Mathematics in 2017, "for contributions to discrete mathematics and theory of computing, particularly random graphs and networks, Ramsey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonid Libkin
Leonid Libkin is a computer scientist who works in data management, in particular in database theory, and in logic in computer science. Libkin is a professor at the University of Edinburgh, where he is chair of Foundations of Data Management in the School of Informatics, He previously worked at Bell Labs, at the University of Toronto, and at the École Normale Supérieure in Paris. Libkin is the author of standard textbooks on finite model theory and on data exchange. He is an ACM Fellow, a Fellow of the Royal Society of Edinburgh, and a member of Academia Europaea. He won best paper awards at the Symposium on Principles of Database Systems (ACM PODS) in 1999, 2003, and 2005, at International Conference on Database Theory (ICDT) in 2011, at the Principles of Knowledge Representation and Reasoning Conference in 2014 and 2018., at the ACM SIGMOD Conference (industry track) in 2023, and a test of time award at ICDT in 2023. He was program chair of ICDT in 2005, PODS in 2007 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modal Logic
Modal logic is a kind of logic used to represent statements about Modality (natural language), necessity and possibility. In philosophy and related fields it is used as a tool for understanding concepts such as knowledge, obligation, and causality, causation. For instance, in epistemic modal logic, the well-formed_formula, formula \Box P can be used to represent the statement that P is known. In deontic modal logic, that same formula can represent that P is a moral obligation. Modal logic considers the inferences that modal statements give rise to. For instance, most epistemic modal logics treat the formula \Box P \rightarrow P as a Tautology_(logic), tautology, representing the principle that only true statements can count as knowledge. However, this formula is not a tautology in deontic modal logic, since what ought to be true can be false. Modal logics are formal systems that include unary operation, unary operators such as \Diamond and \Box, representing possibility and necessi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modal μ-calculus
In theoretical computer science, the modal μ-calculus (Lμ, Lμ, sometimes just μ-calculus, although this can have a more general meaning) is an extension of propositional modal logic (with many modalities) by adding the least fixed point operator μ and the greatest fixed point operator ν, thus a fixed-point logic. The (propositional, modal) μ-calculus originates with Dana Scott and Jaco de Bakker, and was further developed by Dexter Kozen into the version most used nowadays. It is used to describe properties of labelled transition systems and for verifying these properties. Many temporal logics can be encoded in the μ-calculus, including CTL* and its widely used fragments—linear temporal logic and computational tree logic. An algebraic view is to see it as an algebra of monotonic functions over a complete lattice, with operators consisting of functional composition plus the least and greatest fixed point operators; from this viewpoint, the modal μ-calculus is o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model-checking
In computer science, model checking or property checking is a method for checking whether a finite-state model of a system meets a given specification (also known as correctness). This is typically associated with hardware or software systems, where the specification contains liveness requirements (such as avoidance of livelock) as well as safety requirements (such as avoidance of states representing a system crash). In order to solve such a problem algorithmically, both the model of the system and its specification are formulated in some precise mathematical language. To this end, the problem is formulated as a task in logic, namely to check whether a structure satisfies a given logical formula. This general concept applies to many kinds of logic and many kinds of structures. A simple model-checking problem consists of verifying whether a formula in the propositional logic is satisfied by a given structure. Overview Property checking is used for verification when two de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applications Of Parity Games
Application may refer to: Mathematics and computing * Application software, computer software designed to help the user to perform specific tasks ** Application layer, an abstraction layer that specifies protocols and interface methods used in a communications network * Function application, in mathematics and computer science Processes and documents * Application for employment, a form or forms that an individual seeking employment must fill out * College application, the process by which prospective students apply for entry into a college or university * Patent application, a document filed at a patent office to support the grant of a patent Other uses * Application (virtue), a characteristic encapsulated in diligence * Topical application, the spreading or putting of medication to body surfaces See also * * Apply In mathematics and computer science, apply is a function that applies a function to arguments. It is central to programming languages derived from lambda calcul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strongly Connected Component
In the mathematics, mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachability, reachable from every other vertex. The strongly connected components of a directed graph form a partition of a set, partition into subgraph (graph theory), subgraphs that are themselves strongly connected. It is possible to test the strong connectivity (graph theory), connectivity of a graph, or to find its strongly connected components, in linear time (that is, Θ(''V'' + ''E'')). Definitions A directed graph is called strongly connected if there is a path (graph theory), path in each direction between each pair of vertices of the graph. That is, a path exists from the first vertex in the pair to the second, and another path exists from the second vertex to the first. In a directed graph ''G'' that may not itself be strongly connected, a pair of vertices ''u'' and ''v'' are said to be strongly connected to each other if there is a path in ... [...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] |
