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Abstract Family Of Acceptors
An abstract family of acceptors (AFA) is a grouping of generalized acceptors. Informally, an acceptor is a device with a finite state control, a finite number of input symbols, and an internal store with a read and write function. Each acceptor has a start state and a set of accepting states. The device reads a sequence of symbols, transitioning from state to state for each input symbol. If the device ends in an accepting state, the device is said to accept the sequence of symbols. A family of acceptors is a set of acceptors with the same type of internal store. The study of AFA is part of AFL ( abstract families of languages) theory.Seymour Ginsburg, ''Algebraic and automata theoretic properties of formal languages'', North-Holland, 1975, . Formal definitions AFA Schema An ''AFA Schema'' is an ordered 4-tuple (\Gamma, I, f, g), where # \Gamma and I are nonempty abstract sets. # f is the ''write'' function: f : \Gamma^* \times I \rightarrow \Gamma^* \cup \ (N.B. * is the Kleene st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite State Machine
A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of '' states'' at any given time. The FSM can change from one state to another in response to some inputs; the change from one state to another is called a ''transition''. An FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition. Finite-state machines are of two types— deterministic finite-state machines and non-deterministic finite-state machines. A deterministic finite-state machine can be constructed equivalent to any non-deterministic one. The behavior of state machines can be observed in many devices in modern society that perform a predetermined sequence of actions depending on a sequence of events with which they are presented. Simple examples are vending machines, which dispense ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ar ... [...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] |
Kleene Star
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 arbitr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transitive Closure
In mathematics, the transitive closure of a binary relation on a set is the smallest relation on that contains and is transitive. For finite sets, "smallest" can be taken in its usual sense, of having the fewest related pairs; for infinite sets it is the unique minimal transitive superset of . For example, if is a set of airports and means "there is a direct flight from airport to airport " (for and in ), then the transitive closure of on is the relation such that means "it is possible to fly from to in one or more flights". Informally, the ''transitive closure'' gives you the set of all places you can get to from any starting place. More formally, the transitive closure of a binary relation on a set is the transitive relation on set such that contains and is minimal; see . If the binary relation itself is transitive, then the transitive closure is that same binary relation; otherwise, the transitive closure is a different relation. Conversely, transit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite State Automata
A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of '' states'' at any given time. The FSM can change from one state to another in response to some inputs; the change from one state to another is called a ''transition''. An FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition. Finite-state machines are of two types— deterministic finite-state machines and non-deterministic finite-state machines. A deterministic finite-state machine can be constructed equivalent to any non-deterministic one. The behavior of state machines can be observed in many devices in modern society that perform a predetermined sequence of actions depending on a sequence of events with which they are presented. Simple examples are vending machines, which dispense p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pushdown Automata
In the theory of computation, a branch of theoretical computer science, a pushdown automaton (PDA) is a type of automaton that employs a stack. Pushdown automata are used in theories about what can be computed by machines. They are more capable than finite-state machines but less capable than Turing machines (see below). Deterministic pushdown automata can recognize all deterministic context-free languages while nondeterministic ones can recognize all context-free languages, with the former often used in parser design. The term "pushdown" refers to the fact that the stack can be regarded as being "pushed down" like a tray dispenser at a cafeteria, since the operations never work on elements other than the top element. A stack automaton, by contrast, does allow access to and operations on deeper elements. Stack automata can recognize a strictly larger set of languages than pushdown automata. A nested stack automaton allows full access, and also allows stacked values to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Southern California
, mottoeng = "Let whoever earns the palm bear it" , religious_affiliation = Nonsectarian—historically Methodist , established = , accreditation = WSCUC , type = Private research university , academic_affiliations = , endowment = $8.12 billion (2021)As of June 30, 2021. , budget = $6.2 billion (2020–21) , president = Carol Folt , students = 49,318 (2021) , undergrad = 20,790 (2021) , postgrad = 28,528 (2021) , faculty = 4,706 (2021) , administrative_staff = 16,614 (2021) , city = , state = , country = United States , campus = Large City University Park campus, [...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] |
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. Endo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE
The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operations center in Piscataway, New Jersey. The mission of the IEEE is ''advancing technology for the benefit of humanity''. The IEEE was formed from the amalgamation of the American Institute of Electrical Engineers and the Institute of Radio Engineers in 1963. Due to its expansion of scope into so many related fields, it is simply referred to by the letters I-E-E-E (pronounced I-triple-E), except on legal business documents. , it is the world's largest association of technical professionals with more than 423,000 members in over 160 countries around the world. Its objectives are the educational and technical advancement of electrical and electronic engineering, telecommunications, computer engineering and similar disciplines. History Ori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Languages
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of symbols, letters, or tokens that concatenate into strings of the language. Each string concatenated from symbols of this alphabet is called a word, and the words that belong to a particular formal language are sometimes called ''well-formed words'' or ''well-formed formulas''. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar, which consists of its formation rules. In computer science, formal languages are used among others as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages in which the words of the language represent concepts that are associated with particular meanings or semantics. In computational complexit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
