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Topic: Computability theory (computation)

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	Introduction to Theory of Computation, Computation Fundamentals Theory.
		Introduction to Theory of Computation, Computation Fundamentals Theory.
		Computability theory deals primarily with the question of whether a problem is solvable at all on a computer.
		Computability theory is closely related to the branch of mathematical logic called recursion theory, which removes the restriction of studying only models of computation which are close to physically realizable.
	www.activesign.net /theory_computation.php (1279 words)

	Computation - Wikipedia, the free encyclopedia
		However, the meaning of the word computer should be understood in a large sense, since it doese not restrict to a digital computer.
		In computer science, which is sometimes described as the discipline that studies computations, mathematical models of computers are defined; a typical model is the Turing machine.
		The sub-field of computer science which studies mathematical models of computations is called the theory of computation.
	en.wikipedia.org /wiki/Computation (182 words)

	Learn more about Computation in the online encyclopedia. (Site not responding. Last check: )
		Computation can be actually defined as finding a solution to a problem from given inputs by means of an algorithm.
		For thousands of years, computing was done with pen and paper, or chalk and slate, or mentally, sometimes with the aid of tables.
		One way to measure the power of a computational model is to study the class of formal languages that the model can generate; this leads to the Chomsky hierarchy of languages.
	www.onlineencyclopedia.org /c/co/computation.html (772 words)

	Computability theory - Wikipedia (Site not responding. Last check: )
		Computability theory is that part of the theory of computation dealing with which problems are solvable by algorithms (equivalently, by Turing machines), with various restrictions and extensions.
		See the article on theory of computation for a chart showing which classes of problems are subsets of other classes.
		Electronic computers, and even quantum computers, are exactly equivalent to Turing machines, if they have access to an unbounded supply of memory.
	wikipedia.findthelinks.com /co/Computability_theory.html (748 words)

	Course Technology -Introduction to the Theory of Computation, Second Edition (9780534950972)
		Introduction to the Theory of Computation, Second Edition
		Uses a student-friendly approach to teach computer theory.
		Michael Sipser has taught theoretical computer science and other mathematical subjects at the Massachusetts Institute of Technology for the past 25 years, where he is a professor of Applied Mathematics and a member of the Computer Science and Artificial Intelligence Laboratory (CSAIL).
	www.course.com /catalog/product.cfm?isbn=0-534-95097-3&CFID=5278206&CFTOKEN=94907853 (243 words)

	COMPUTABILITY LOGIC: a theory of interactive computation HOMEPAGE
		Computability is certainly one of the most interesting and fundamental concepts in mathematics and computer science, and it would be more than natural to ask what logic it induces.
		Computability logic is a formal theory of (interactive) computability in the same sense as classical logic is a formal theory of truth.
		Computability logic (CL) is a systematic formal theory of computational tasks and resources, which, in a sense, can be seen as a semantics-based alternative to (the syntactically introduced) linear logic.
	www.cis.upenn.edu /~giorgi/cl.html (3989 words)

	Computation (Site not responding. Last check: )
		To facilitate computations, it is noted that in standard association...
		Computation can be defined as finding a solution to a problem from given inputs by means of an algorithm.
		The theory of computation studies these models of general computation, along with the limits of computing: Which problems are (probably) unsolvable by a computer?
	hallencyclopedia.com /Computation (927 words)

	Theoretical Computer Science and You
		Computers can be mechanical-a computer was built at MIT completely out of tinkertoys which could play tic-tac-toe.
		While all of the above types of computers use different types of "life blood" for their computations, they are all pretty similar in that they all use logic gates.
		Some researchers are experimenting with chemical and biological computers where the computation occurs as a result of a chemical reaction or the proliferation of a certain strain of unicellular organism.
	www.cs.unm.edu /~saia/computability.html (1373 words)

	Computability Theory (Site not responding. Last check: )
		Post in the 1930's, and includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, subrecursive hierarchy classifications, computable structures, and complexity theory relating to the preceding.
		There is also a Computability and Complexity in Analysis network, and one for Foundations of Mathematics, some of whose discussions relate to computability theory.
		Logic Colloquium '97 (the 1997 European Meeting of the Association of Symbolic Logic) was held in Leeds, and a substantial part of the programme was devoted to computability theory and related topics.
	www.amsta.leeds.ac.uk /pure/staff/cooper/research.html (553 words)

	CS520: An Introduction to the Theory of Computation (Site not responding. Last check: )
		This course is an introduction to the theory of computation.
		This material is central to many branches of computer science; it underlies the basic theory of compiler design, the efficiency of algorithms, and the limitations of computing.
		Computer programming skills and experience might be helpful in guiding intuition, but primarily students are expected to exercise mathematical reasoning and logical deduction.
	www.cs.wisc.edu /~jyc/cs520.html (705 words)

	Amazon.co.uk: Computability Theory: Books (Site not responding. Last check: )
		This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications.
		The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context.
		Computability and Unsolvability in the real world is also discussed, along with the search for natural examples of incomputable sets, a topic which is currently more interesting than ever.
	www.amazon.co.uk /exec/obidos/ASIN/1584882379 (899 words)

	Theory of Computation (Site not responding. Last check: )
		Its reflection mechanism provides a basis for the theory of computational complexity which we are striving to integrate usefully as an aspect of any theorem with computational meaning.
		In this case, the applied mathematics is linked to computers by a law of information science, the law is that certain abstract models of computing faithfully model what is feasible to compute in the real world with devices of a certain structure.
		Indeed the whole chain of reasoning could be formalized in type theory and related to the physical world by laws of device physics, celestial mechanics, computer science and mathematics.
	www.cs.cornell.edu /Info/Projects/NuPrl/Intro/Theory/theory.html (996 words)

	Computability theory - Encyclopedia.WorldSearch (Site not responding. Last check: )
		Computability and Complexity Theory (Texts in Computer Science)
		Computability, Complexity, and Languages, Second Edition : Fundamentals of Theoretical Computer Science (Computer Science and Scientific Computing)
		Computability and Complexity: From a Programming Perspective (Foundations of Computing)
	encyclopedia.worldsearch.com /computability_theory.htm (707 words)

	R010800A: Computation Theory Definitions, Nomenclature, and Elementary Concepts
		Theories of computability and complexity require a precise definition of a computer.
		Computability theory introduces several of the concepts used in complexity theory [Sipser1997].
		For now, it is important to understand that propositions in the form used in propositional algebra are the consequence of analysis of statements as to their sense.
	nfocentrale.net /miser/readings/R010800A.htm (1071 words)

	Computability and Complexity
		In addition, there is an extensive classification of computable problems into computational complexity classes according to how much computation — as a function of the size of the problem instance — is needed to answer that instance.
		He finally used the primitive recursive functions to compute properties of the represented formulas including that a formula was well formed, a sequence of formulas was a proof, and that a formula was a theorem.
		The first important insight in complexity theory is that a good measure of the complexity of an algorithm is its asymptotic worst-case complexity as a function of the size of the input, n.
	plato.stanford.edu /entries/computability (5266 words)

	CS487 : Theory of Computation
		Computability Theory ("What can or cannot be computed?") and Complexity Theory ("How efficient can a certain computation be?").
		An introduction to complexity issues in application areas such as robotics, graphics, compilers, and computer security.Prerequisites COS 341.
		The text will be Theory of Computation by Michael Sipser, printed by PWS publishing.
	www.cs.princeton.edu /courses/archive/fall98/cs487 (260 words)

	Re: Lambda calculus w/theory of computation
		Computability is done from the point of view of WHILE programs and a functional languages, and looks quite attractive: N.D. Jones,Computability and Complexity: From a Programming Perspective.
		The way computation is expressed (reducing any subterm until no redexes remain) makes it very different from what we are used to, and makes it necessary to prove Church-Rosser.
		I taught a Theory of Computation class with it and found that it covers regular languages extremely well but is not doing such a great job on context-free languages.
	www.seas.upenn.edu /~sweirich/types/archive/1999-2003/msg01036.html (2772 words)

	COT 6421 - Theory of Computation II (Site not responding. Last check: )
		Advanced computability theory; diagonalization and reductions; applications of computability theory to logic; computational complexity; the classes P, NP, and PSPACE; polynomial-time reductions and completeness.
		Computability Theory: undecidability; mapping reducibility; Gödel's Incompleteness Theorem; decidability of Presburger arithmetic.
		Michael Sipser, Introduction to the Theory of Computation, (Brooks Cole, 1997).
	www.cs.fiu.edu /~ege/grad/theory/COT6421.html (113 words)

	Computability Theory
		Lewis and C. Papadimitriou, Elements of the Theory of Computation, Prentice-Hall, 1981.
		Epstein and W. Carnielli, Computability: Computable functions, logic, and foundations of mathematics, Wadsworth and Brooks, 1989.
		Sipser, Introduction to the Theory of Computation, PWS, 1997.
	www.cco.caltech.edu /~sugao/macs117a.htm (608 words)

	Computability Theory (Site not responding. Last check: )
		Their influence extends beyond the practical, and investigations into the nature and power of computation have spawned many areas of academic inquiry.
		We want to single out those functions which are computable, meaning that there is some fixed algorithm which, given any input, produces the correct output.
		For example, the function that takes two natural numbers x and y as input, and gives the value x+y as output, should be a computable function (since the mechanical procedure that we learned in grade school suffices).
	www.math.uchicago.edu /~mileti/museum/computability.html (442 words)

	Computability Science, Directory (Site not responding. Last check: )
		Computability Theory Directory of researchers working in computability theory, and list of open problems.
		Bibliographic Database for Computability Theory Extensive bibliography on computability and recursion theory, maintained by Peter Cholak.
		ECCC - Electronic Colloquium on Computational Complexity The Electronic Colloquium on Computational Complexity is a new forum for the rapid and widespread interchange of ideas, techniques, and research in computational complexity.
	www.indiapolicyinstitute.org /aW5kXzI2OTIw.aspx (175 words)

	No Title (Site not responding. Last check: )
		We shall develop the Theory of Computability with an eye toward elucidating the formal limits to the power of digital computers and computation thereon.
		The crescendo of this development will be a theorem that, stated (very) informally, asserts the impossibility of determining anything about the dynamic behavior of programs from their static descriptions.
		We shall introduce Complexity Theory as a "resource-bounded" extension of Computability Theory.
	www.cs.umass.edu /~rsnbrg/cs401/cs401.html (540 words)

	Directory - Science: Math: Logic and Foundations: Computability (Site not responding. Last check: )
		Computability Theory · cached · Directory of researchers working in computability theory, and list of open problems.
		Bibliographic Database for Computability Theory · cached · Extensive bibliography on computability and recursion theory, maintained by Peter Cholak.
		Computability and Complexity in Analysis Network · cached · The CCA Network provides some useful information for researchers working in the field of computability and complexity in analysis.
	www.incywincy.com /default?p=26920 (232 words)

	Computability theory - Wikipedia, the free encyclopedia
		A branch of mathematical logic, traditionally called recursion theory
		A branch of the theory of computation; see computability theory (computation)
		This is a disambiguation page — a list of articles associated with the same title.
	en.wikipedia.org /wiki/Computability_theory (84 words)

	Mathematics and Computation
		Computer algebra systems (CAS), such as Mathematica, are complex systems that have been evolving for a couple of decades.
		Consequently, there have been a number of presentations of computability theory that aimed to present the subject in an abstract and conceptually pleasing way.
		As the paper aims to be a self-contained introduction to ASD for those interested in constructive and computable topology and analysis, it includes a rapid survey of the ASD calculus.
	math.andrej.com (1167 words)

	Jon Feldman (Site not responding. Last check: )
		I taught "Introduction to Coding Theory" in Fall, 2004 at Columbia.
		I taught "Theory of Computation" in Spring, 2005 at Columbia.
		I am teaching "Theory of Computation" in Fall, 2005 at Columbia.
	www.columbia.edu /~jf2189 (128 words)

	kohlenb (Site not responding. Last check: )
		This course is an introduction to computability in higher types and computability over general structures.
		Classical recursion theory studies properties of computable functions and various equivalent characterizations of computability but also computability relative to certain non-recursive objects.
		Kleene introduced in 1959 an extension of the notation of computation to all functionals of finite type (S1-S9 computability) which allows to define algorithms relative to higher type oracles and at the same time defines a class of computable object for all finite types.
	www.daimi.au.dk /~kohlenb/course9.html (339 words)

	Readings: Theory of Computation
		As I have continued to explore mathematical logic as a context for computation theory and the Miser Project, I am now inclined to classify most of these papers as strongly centered in mathematical logic and as less specific to computation, even the seminal work of Turing.
		This is a primary reference in the theory of computation.
		Although it does not address Church's Thesis and effective computability, it is widely used for its mapping of the foundation of computation theory.
	nfocentrale.net /miser/readings/theory.htm (1816 words)

	Amazon.com: Introduction to the Theory of Computation: Books (Site not responding. Last check: )
		Computers and Intractability : A Guide to the Theory of NP-Completeness (Series of Books in the Mathematical Sciences) by M.
		The theory of computation represents a fascinating landscape that intersects computer science and mathematics and can be roughly divided into three overlapping areas: automata and formal languages, computability theory, and computational complexity.
		For example, most books on computability theory do not discuss automata outside of Turing machines, but in his book Sipser elegantly proves that the equivalence problem is decidable for deterministic finite automata, but undecidable for pushdown automata.
	www.amazon.com /exec/obidos/tg/detail/-/053494728X?v=glance (1998 words)

	Amazon.com: Computability and Complexity Theory (Texts in Computer Science): Books: Steven Homer,Alan L. Selman (Site not responding. Last check: )
		This volume introduces materials that are the core knowledge in the theory of computation.
		The book is self-contained, with a preliminary chapter describing key mathematical concepts and notations and subsequent chapters moving from the qualitative aspects of classical computability theory to the quantitative aspects of complexity theory.
		Dedicated chapters on undecidability, NP-completeness, and relative computability round off the work, which focuses on the limitations of computability and the distinctions between feasible and intractable.
	www.amazon.com /exec/obidos/tg/detail/-/0387950559?v=glance (1060 words)

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