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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 se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automata Theory
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science. The word ''automata'' comes from the Greek word αὐτόματος, which means "self-acting, self-willed, self-moving". An automaton (automata in plural) is an abstract self-propelled computing device which follows a predetermined sequence of operations automatically. An automaton with a finite number of states is called a Finite Automaton (FA) or Finite-State Machine (FSM). The figure on the right illustrates a finite-state machine, which is a well-known type of automaton. This automaton consists of states (represented in the figure by circles) and transitions (represented by arrows). As the automaton sees a symbol of input, it makes a transition (or jump) to another state, according to its transition function, which takes the previous state and current input symbol as its arguments. Automata theo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parity Automaton
Parity may refer to: * Parity (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 * 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 * 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, respectivel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
European Summer School In Logic, Language And Information
The European Summer School in Logic, Language and Information (ESSLLI) is an annual academic conference organized by the European Association for Logic, Language and Information. The focus of study is the "interface between linguistics, logic and computation, with special emphasis on human linguistic and cognitive ability"."ESSLLI – Aims" , (). The conference is held over two weeks of the European Summer, and offers about 50 courses at introductory and advanced levels. It attracts around 500 participants from all over the world. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Büchi Automata
Buchi can mean: __NOTOC__ Items *Bachi, special Japanese drumsticks *Butsi, the Hispanised term for jin deui (pastry made from glutinous rice) in the Philippines *Büchi automaton, finite state automata extended to infinite inputs *Büchi arithmetic, a mathematical logical fragment People Given names *Buchi Atuonwu, Nigerian reggae gospel artist *Buchi (comedian), stage name of Onyebuchi Ojieh, Nigerian comedian *Buchi Emecheta, (d. 2017) Nigerian British writer Family names *George Büchi (1921–1998), an organic chemist *Julius Richard Büchi (1924–1984), developer of the Büchi automaton *Hernán Büchi (born 1949), Finance Minister of Chile (1985–1989) *Albert Büchi (1907–1988), a Swiss professional road bicycle racer Nicknames *Yutaka Izubuchi, anime designer and director *Nigerian Igbo first names such as Onyebuchi, Nnabuchi, Maduabuchi, a suffix that translates as "...is God." Fictional characters *Buchi in ''One Piece ''One Piece'' (stylized in all ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Büchi Automaton
In computer science and automata theory, a deterministic Büchi automaton is a theoretical machine which either accepts or rejects infinite inputs. Such a machine has a set of states and a transition function, which determines which state the machine should move to from its current state when it reads the next input character. Some states are accepting states and one state is the start state. The machine accepts an input if and only if it will pass through an accepting state infinitely many times as it reads the input. A non-deterministic Büchi automaton, later referred to just as a Büchi automaton, has a transition function which may have multiple outputs, leading to many possible paths for the same input; it accepts an infinite input if and only if some possible path is accepting. Deterministic and non-deterministic Büchi automata generalize deterministic finite automata and nondeterministic finite automata to infinite inputs. Each are types of ω-automata. Büchi automata rec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Streett Automaton
{{disambiguation ...
Streett may refer to: People * Abraham J. Streett, American politician * Harry Streett Baldwin (1894–1952), U.S. Congressman from 1943 to 1947 * Joseph M. Streett (1838–1921), American politician and newspaper editor * St. Clair Streett (1893–1970), United States Air Force major general and writer who first organized and led the Strategic Air Command Other uses * Col. John Streett House, historic home located at Street, Harford County, Maryland, United States * Streett automaton, a class of ω-automaton, a variation of finite automaton that runs on infinite, rather than finite, strings as input See also *Streat *Street *Strete Strete is a village and civil parish in the South Hams district of Devon, England, on the coast of Start Bay, within the South Devon Area of Outstanding Natural Beauty. The village is about 5 miles south-west of the town of Dartmouth on the ... [...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 painter * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ω-automaton
In automata theory, a branch of theoretical computer science, an ω-automaton (or stream automaton) is a variation of finite automata 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 automata, Rabin automata, Streett automata, parity automata and Muller automata, each deterministic or non-deterministic. These classes of ω-automata differ only in terms of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ω-automaton
In automata theory, a branch of theoretical computer science, an ω-automaton (or stream automaton) is a variation of finite automata 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 automata, Rabin automata, Streett automata, parity automata and Muller automata, each deterministic or non-deterministic. These classes of ω-automata differ only in terms of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Powerset
In mathematics, the power set (or powerset) of a set is the set of all subsets of , including the empty set and itself. In axiomatic set theory (as developed, for example, in the ZFC axioms), the existence of the power set of any set is postulated by the axiom of power set. The powerset of is variously denoted as , , , \mathbb(S), or . The notation , meaning the set of all functions from S to a given set of two elements (e.g., ), is used because the powerset of can be identified with, equivalent to, or bijective to the set of all the functions from to the given two elements set. Any subset of is called a ''family of sets'' over . Example If is the set , then all the subsets of are * (also denoted \varnothing or \empty, the empty set or the null set) * * * * * * * and hence the power set of is . Properties If is a finite set with the cardinality (i.e., the number of all elements in the set is ), then the number of all the subsets of is . This fact as well ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Set
In mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle count and finish counting. For example, :\ is a finite set with five elements. The number of elements of a finite set is a natural number (possibly zero) and is called the '' cardinality (or the cardinal number)'' of the set. A set that is not a finite set is called an ''infinite set''. For example, the set of all positive integers is infinite: :\. Finite sets are particularly important in combinatorics, the mathematical study of counting. Many arguments involving finite sets rely on the pigeonhole principle, which states that there cannot exist an injective function from a larger finite set to a smaller finite set. Definition and terminology Formally, a set is called finite if there exists a bijection :f\colon S\to\ for some natural number . The number is the set's cardinality, denoted as . The empty set o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
