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Abstract Family Of Languages
In computer science, in particular in the field of formal language theory, an abstract family of languages is an abstract mathematical notion generalizing characteristics common to the regular languages, the context-free languages and the recursively enumerable languages, and other families of formal languages studied in the scientific literature. Formal definitions A ''formal language'' is a set for which there exists a finite set of abstract symbols such that L \subseteq\Sigma^*, where * is the Kleene star operation. A ''family of languages'' is an ordered pair (\Sigma,\Lambda), where # is an infinite set of symbols; # is a set of formal languages; # For each in there exists a finite subset \Sigma_1 \subset \Sigma such that L \subseteq \Sigma_1^*; and # for some in . A ''trio'' is a family of languages closed under e-free homomorphism, inverse homomorphism, and intersection with regular language. A ''full trio,'' also called a ''cone,'' is a trio closed under arbitra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. 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 for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kleene Plus
In mathematical logic and computer science, the Kleene star (or Kleene operator or Kleene closure) is a unary operation, either on sets of strings or on sets of symbols or characters. In mathematics, it is more commonly known as the free monoid construction. The application of the Kleene star to a set V is written as ''V^*''. It is widely used for regular expressions, which is the context in which it was introduced by Stephen Kleene to characterize certain automata, where it means "zero or more repetitions". # If V is a set of strings, then ''V^*'' is defined as the smallest superset of V that contains the empty string \varepsilon and is closed under the string concatenation operation. # If V is a set of symbols or characters, then ''V^*'' is the set of all strings over symbols in V, including the empty string \varepsilon. The set ''V^*'' can also be described as the set containing the empty string and all finite-length strings that can be generated by concatenating arbitrary e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Introduction To Automata Theory, Languages, And Computation
''Introduction to Automata Theory, Languages, and Computation'' is an influential computer science textbook by John Hopcroft and Jeffrey Ullman on formal languages and the theory of computation. Rajeev Motwani contributed to later editions beginning in 2000. Nickname The Jargon File records the book's nickname, ''Cinderella Book'', thusly: "So called because the cover depicts a girl (putatively Cinderella) sitting in front of a Rube Goldberg device and holding a rope coming out of it. On the back cover, the device is in shambles after she has (inevitably) pulled on the rope." Edition history and reception The forerunner of this book appeared under the title ''Formal Languages and Their Relation to Automata'' in 1968. Forming a basis both for the creation of courses on the topic, as well as for further research, that book shaped the field of automata theory for over a decade, cf. (Hopcroft 1989). * * * * * The first edition of ''Introduction to Automata Theory, Languag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symposium On Switching And Automata Theory
The IEEE Annual Symposium on Foundations of Computer Science (FOCS) is an academic conference in the field of theoretical computer science. FOCS is sponsored by the IEEE Computer Society. As writes, FOCS and its annual Association for Computing Machinery counterpart STOC (the Symposium on Theory of Computing) are considered the two top conferences in theoretical computer science, considered broadly: they “are forums for some of the best work throughout theory of computing that promote breadth among theory of computing researchers and help to keep the community together.” includes regular attendance at FOCS and STOC as one of several defining characteristics of theoretical computer scientists. Awards The Knuth Prize for outstanding contributions to theoretical computer science is presented alternately at FOCS and STOC. Works of the highest quality presented at the conference are awarded the Best Paper Award. In addition, the Machtey Award is presented to the best student- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher learning in the United States and one of the most prestigious and highly ranked universities in the world. The university is composed of ten academic faculties plus Harvard Radcliffe Institute. The Faculty of Arts and Sciences offers study in a wide range of undergraduate and graduate academic disciplines, and other faculties offer only graduate degrees, including professional degrees. Harvard has three main campuses: the Cambridge campus centered on Harvard Yard; an adjoining campus immediately across Charles River in the Allston neighborhood of Boston; and the medical campus in Boston's Longwood Medical Area. Harvard's endowment is valued at $50.9 billion, making it the wealthiest academic institution in the world. Endowment inco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sheila Greibach
Sheila Adele Greibach (born 6 October 1939 in New York City) is a researcher in formal languages in computing, automata, compiler theory and computer science. She is an Emeritus Professor of Computer Science at the University of California, Los Angeles, and notable work include working with Seymour Ginsburg and Michael A. Harrison in context-sensitive parsing using the stack automaton model. Besides establishing the normal form (Greibach normal form) for context-free grammars, in 1965, she also investigated properties of W-grammars, pushdown automata, and decidability problems. Early career Greibach earned an A.B. degree (summa cum laude) in Linguistics and Applied Mathematics from Radcliffe College in 1960, and two years after achieved an A.M. degree. In 1963, she was awarded a PhD at Harvard University, advised by Anthony Oettinger with a PhD thesis entitled "Inverses of Phrase Structure Generators". She continued to work at Harvard at the Division of Engineering and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Southern California
The University of Southern California (USC, SC, or Southern Cal) is a Private university, private research university in Los Angeles, California, United States. Founded in 1880 by Robert M. Widney, it is the oldest private research university in California. The university is composed of one Liberal arts education, liberal arts school, the University of Southern California academics, Dornsife College of Letters, Arts and Sciences, and 22 Undergraduate education, undergraduate, Graduate school, graduate, and professional schools, enrolling roughly 21,000 undergraduate and 28,500 Postgraduate education, post-graduate students from all 50 U.S. states and more than 115 countries. It is also a member of the Association of American Universities, which it joined in 1969. USC is ranked as one of the top universities in the United States and admission to its programs is considered College admissions in the United States, highly selective. USC has graduated more alumni who have gone on to w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seymour Ginsburg
Seymour Ginsburg (December 12, 1927 – December 5, 2004) was an American pioneer of automata theory, formal language theory, and database theory, in particular; and computer science, in general. His work was influential in distinguishing theoretical Computer Science from the disciplines of Mathematics and Electrical Engineering. During his career, Ginsburg published over 100 papers and three books on various topics in theoretical Computer Science. Biography Seymour Ginsburg received his B.S. from City College of New York in 1948, where along with fellow student Martin Davis he attended an honors mathematics class taught by Emil Post. He earned a Ph.D. in Mathematics from the University of Michigan in 1952, studying under Ben Dushnik. Ginsburg's professional career began in 1951 when he accepted a position as assistant professor of mathematics at the University of Miami in Coral Gables, Florida. He turned his attention wholly towards computer science in 1955 when he moved ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recursive Language
In mathematics, logic and computer science, a formal language (a set of finite sequences of symbols taken from a fixed alphabet) is called recursive if it is a recursive subset of the set of all possible finite sequences over the alphabet of the language. Equivalently, a formal language is recursive if there exists a total Turing machine (a Turing machine that halts for every given input) that, when given a finite sequence of symbols as input, accepts it if it belongs to the language and rejects it otherwise. Recursive languages are also called decidable. The concept of decidability may be extended to other models of computation. For example, one may speak of languages decidable on a non-deterministic Turing machine. Therefore, whenever an ambiguity is possible, the synonym used for "recursive language" is Turing-decidable language, rather than simply ''decidable''. The class of all recursive languages is often called R, although this name is also used for the class RP. This ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Context-sensitive Language
In formal language theory, a context-sensitive language is a language that can be defined by a context-sensitive grammar (and equivalently by a noncontracting grammar). Context-sensitive is one of the four types of grammars in the Chomsky hierarchy. Computational properties Computationally, a context-sensitive language is equivalent to a linear bounded nondeterministic Turing machine, also called a linear bounded automaton. That is a non-deterministic Turing machine with a tape of only kn cells, where n is the size of the input and k is a constant associated with the machine. This means that every formal language that can be decided by such a machine is a context-sensitive language, and every context-sensitive language can be decided by such a machine. This set of languages is also known as NLINSPACE or NSPACE(''O''(''n'')), because they can be accepted using linear space on a non-deterministic Turing machine. The class LINSPACE (or DSPACE(''O''(''n''))) is defined the same, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chomsky Hierarchy
In formal language theory, computer science and linguistics, the Chomsky hierarchy (also referred to as the Chomsky–Schützenberger hierarchy) is a containment hierarchy of classes of formal grammars. This hierarchy of grammars was described by Noam Chomsky in 1956. It is also named after Marcel-Paul Schützenberger, who played a crucial role in the development of the theory of formal languages. Formal grammars A formal grammar of this type consists of a finite set of '' production rules'' (''left-hand side'' → ''right-hand side''), where each side consists of a finite sequence of the following symbols: * a finite set of ''nonterminal symbols'' (indicating that some production rule can yet be applied) * a finite set of ''terminal symbols'' (indicating that no production rule can be applied) * a ''start symbol'' (a distinguished nonterminal symbol) A formal grammar provides an axiom schema for (or ''generates'') a ''formal language'', which is a (usually infinite) s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concatenation
In formal language, formal language theory and computer programming, string concatenation is the operation of joining character string (computer science), character strings wikt:end-to-end, end-to-end. For example, the concatenation of "snow" and "ball" is "snowball". In certain formalisations of concatenation theory, also called string theory, string concatenation is a primitive notion. Syntax In many programming languages, string concatenation is a binary operation, binary infix operator. The + (plus) operator is often operator overloading, overloaded to denote concatenation for string arguments: "Hello, " + "World" has the value "Hello, World". In other languages there is a separate operator, particularly to specify implicit type conversion to string, as opposed to more complicated behavior for generic plus. Examples include . in Edinburgh IMP, Perl, and PHP, .. in Lua (programming language), Lua, and & in Ada, AppleScript, and Visual Basic. Other syntax exists, like ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
