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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, resulting in a (possibly infinite) path, called the 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 ''n'' successors ( S2S for ''n'' = 2), where determi ... [...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, example.edu, second-level domain names reserved for use in documentation as examples * HMS Example (P165), 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), ''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), ''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, an inner suburb of Barcelona wit ... [...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] |
Moshe Y
Moses ( el, Μωϋσῆς),from Latin and Greek Moishe ( yi, משה),from Yiddish Moshe ( he, מֹשֶׁה),from Modern Hebrew or Movses (Armenian: Մովսես) from Armenian is a male given name, after the biblical figure Moses. According to the Torah, the name "Moses" comes from the Hebrew verb, meaning "to pull out/draw out" f water and the infant Moses was given this name by Pharaoh's daughter after she rescued him from the Nile (Exodus 2:10) Since the rise of Egyptology and decipherment of hieroglyphs, it was postulated that the name of Moses, with a similar pronunciation as the Hebrew Moshe, is the Egyptian word for Son, with Pharaoh names such as Thutmose and Ramesses roughly translating to "son of Thoth" and "son of Ra," respectively. There are various ways of pronouncing the Hebrew name of Moses, for example in Ashkenazi western European it would be pronounced Mausheh, in Eastern Europe Moysheh, in northern Islamic countries Moussa, and in Yemen Mesha. The nickname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joel Spencer
Joel Spencer (born April 20, 1946) is an American mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On .... He is a combinatorialist who has worked on probability, 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 Lectures, Erdős Lecturer at Hebrew University of Jerusalem ... [...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, and at the École Normale Supérieure in Paris. He previously worked at the University of Toronto, and at Bell Labs. 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., and at the ACM SIGMOD SIGMOD is the Association for Computing Machinery's Special Interest Group on Management of Data, which specializes in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modal Logic
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other systems by adding unary operators \Diamond and \Box, representing possibility and necessity respectively. For instance the modal formula \Diamond P can be read as "possibly P" while \Box P can be read as "necessarily P". Modal logics can be used to represent different phenomena depending on what kind of necessity and possibility is under consideration. When \Box is used to represent epistemic necessity, \Box P states that P is epistemically necessary, or in other words that it is known. When \Box is used to represent deontic necessity, \Box P states that P is a moral or legal obligation. In the standard relational semantics for modal logic, formulas are assigned truth values relative to a '' possible world''. A formula's truth value ... [...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 des ... [...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 A topical medication is a medication that is applied to a particular place on or in the body. Most often topical medication means application to body surfaces such as the skin or mucous membranes to treat ailments via a large range of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strongly Connected Component
In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. The strongly connected components of an arbitrary directed graph form a partition into subgraphs that are themselves strongly connected. It is possible to test the strong 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 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 each direction between them. The binary relation of being strongly connected is an equivalence relation ... [...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 pain ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NP-hard
In computational complexity theory, NP-hardness ( non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally "at least as hard as the hardest problems in NP". A simple example of an NP-hard problem is the subset sum problem. A more precise specification is: a problem ''H'' is NP-hard when every problem ''L'' in NP can be reduced in polynomial time to ''H''; that is, assuming a solution for ''H'' takes 1 unit time, ''H''s solution can be used to solve ''L'' in polynomial time. As a consequence, finding a polynomial time algorithm to solve any NP-hard problem would give polynomial time algorithms for all the problems in NP. As it is suspected that P≠NP, it is unlikely that such an algorithm exists. It is suspected that there are no polynomial-time algorithms for NP-hard problems, but that has not been proven. Moreover, the class P, in which all problems can be solved in polynomial time, is contained in the NP class. De ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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