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Communicating X-Machine
The Communicating (Stream) X-Machine is a model of computation introduced by various researchers in the 1990s to model systems composed of communicating agents. The model exists in several variants, which are either based directly on Samuel Eilenberg's X-machineS. Eilenberg (1974) ''Automata, Languages and Machines, Vol. A''. Academic Press, London. or on Gilbert Laycock's later Stream X-Machine The Stream X-machine (SXM) is a model of computation introduced by Gilbert Laycock in his 1993 PhD thesis, ''The Theory and Practice of Specification Based Software Testing''.Gilbert Laycock (1993) ''The Theory and Practice of Specification Based ....Gilbert Laycock (1993) ''The Theory and Practice of Specification Based Software Testing''. PhD Thesis, University of Sheffield. Abstract{{Webarchive, url=https://web.archive.org/web/20071105145328/http://www.mcs.le.ac.uk/people/gtl1/PhDabstract.html , date=2007-11-05 References Theory of computation Models of computation< ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Samuel Eilenberg
Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish-American mathematician who co-founded category theory (with Saunders Mac Lane) and homological algebra. Early life and education He was born in Warsaw, Kingdom of Poland to a Jewish family. He spent much of his career as a professor at Columbia University. He earned his Ph.D. from University of Warsaw in 1936, with thesis ''On the Topological Applications of Maps onto a Circle''; his thesis advisors were Kazimierz Kuratowski and Karol Borsuk. He died in New York City in January 1998. Career Eilenberg's main body of work was in algebraic topology. He worked on the axiomatic treatment of homology theory with Norman Steenrod (and the Eilenberg–Steenrod axioms are named for the pair), and on homological algebra with Saunders Mac Lane. In the process, Eilenberg and Mac Lane created category theory. Eilenberg was a member of Bourbaki and, with Henri Cartan, wrote the 1956 book ''Homological Algebra''. La ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
X-machine
The X-machine (''XM'') is a theoretical model of computation introduced by Samuel Eilenberg in 1974.S. Eilenberg (1974) ''Automata, Languages and Machines, Vol. A''. Academic Press, London. The ''X'' in "X-machine" represents the fundamental data type on which the machine operates; for example, a machine that operates on databases (objects of type ''database'') would be a ''database''-machine. The X-machine model is structurally the same as the finite-state machine, except that the symbols used to label the machine's transitions denote relations of type ''X''→''X''. Crossing a transition is equivalent to applying the relation that labels it (computing a set of changes to the data type ''X''), and traversing a path in the machine corresponds to applying all the associated relations, one after the other. Original theory Eilenberg's original X-machine was a completely general theoretical model of computation (subsuming the Turing machine, for example), which admitted determi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stream X-Machine
The Stream X-machine (SXM) is a model of computation introduced by Gilbert Laycock in his 1993 PhD thesis, ''The Theory and Practice of Specification Based Software Testing''.Gilbert Laycock (1993) ''The Theory and Practice of Specification Based Software Testing''. PhD Thesis, University of Sheffield, Dept of Computer Science. {{Webarchive, url=https://web.archive.org/web/20071105145328/http://www.mcs.le.ac.uk/people/gtl1/PhDabstract.html , date=2007-11-05 Based on Samuel Eilenberg's X-machine, an extended finite-state machine for processing data of the type ''X'',Samuel Eilenberg (1974) ''Automata, Languages and Machines, Vol. A''. London: Academic Press. the Stream X-Machine is a kind of X-machine for processing a memory data type ''Mem'' with associated input and output streams ''In''* and ''Out''*, that is, where ''X'' = ''Out''* × ''Mem'' × ''In''*. The transitions of a Stream X-Machine are labelled by functions of the form φ: ''Mem'' × ''In'' → ''Out'' × ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory Of Computation
In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm, how efficiently they can be solved or to what degree (e.g., approximate solutions versus precise ones). The field is divided into three major branches: automata theory and formal languages, computability theory, and computational complexity theory, which are linked by the question: ''"What are the fundamental capabilities and limitations of computers?".'' In order to perform a rigorous study of computation, computer scientists work with a mathematical abstraction of computers called a model of computation. There are several models in use, but the most commonly examined is the Turing machine. Computer scientists study the Turing machine because it is simple to formulate, can be analyzed and used to prove results, and because it represents what many consider the most powerful possible "reasonable" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
