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| | Theory of computation - Wikipedia, the free encyclopedia |
 | | 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. | | | The theory of computation is the branch of computer science that deals with whether and how efficiently problems can be solved on a computer. | | | Computability theory deals primarily with the question of whether a problem is solvable at all on a computer. |
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http://en.wikipedia.org/wiki/Theory_of_computation
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| | Theory of Computation |
| | A very nice essay Computability and Complexity by Jon Kleinberg and Christos Papadimitriou. | | | Theory of computing is the fundamental scientific discipline concerned with understanding (efficient) computational phenomena, whether it be man-made, in nature, or imaginary. | | | The models that we use to understand computation are fundamental, and the conclusions that we draw from them have profound implications about the world in which we live in. |
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http://www.cs.princeton.edu/introcs/70theory
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| | Readings: 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. | | | This is a primary reference in the theory of computation. | | | This is an undergraduate introductory text on the theory of computation. |
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http://nfocentrale.net/miser/readings/theory.htm
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| | Theory of Computation |
| | This course presents an in-depth introduction to the main models and concepts of the mathematical theory of computation, including: Computability, Complexity, and Logic. | | | Harry Lewis and Christos Papadimitriou, Elements of the Theory of Computation, Prentice-Hall, 1981: Chapters 1--3. | | | Michael Sipser, Introduction to the Theory of Computation, 1997: Chapters 1 -- 2. |
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http://www.cs.umass.edu/~immerman/cs601
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| | Conclusion: Mathematical Theory of Computation |
| | The formalism differs from those heretofore used in the theory of computability in its emphasis on cases of proving statements within the system rather than metatheorems about it. | | | In the earlier sections of this paper I have tried to lay a basis for a theory of how computations are built up from elementary operations and also of how data spaces are built up. | | | It is reasonable to hope that the relationship between computation and mathematical logic will be as fruitful in the next century as that between analysis and physics in the last. |
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http://www-formal.stanford.edu/jmc/basis1/node15.html
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| | Bibliographies on Theory/Foundations of Computer Science |
| | Bibliography on Computability, Complexity and Constructivity in Analysis | | | Bibliography of the proceedings volumes of the annual ACM Symposia on the Theory of Computing (STOC) | | | A large bibliography on theory/foundations of computer science |
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http://liinwww.ira.uka.de/bibliography/Theory
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| | COT 4420 Theory of Computation |
| | Finite state automata, Moore and Mealy machines, regular expressions and languages, deterministic and non-deterministic pushdown automata, context free languages, context sensitive languages, normal forms, Turing machines, recursive and recursively enumerable sets, undecidability, introduction to computability and complexity theory. | | | The goal of this course is to provide students with an understanding of basic concepts in the theory of computation. | | | Students will learn about a variety of issues in the mathematical development of computer science theory, particularly finitary representations for languages and machines, as well as gain a more formal understanding of algorithms and procedures. |
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http://www.cs.fsu.edu/~sudhir/courses/2005cot4420
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| | Information on Introduction to the Theory of Computation |
| | Textbook for an upper division undergraduate and introductory graduate level course covering automata theory, computability theory, and complexity theory. | | | Information on Introduction to the Theory of Computation | | | I am no longer maintaining its errata site. |
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http://www-math.mit.edu/~sipser/book.html
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| | Encyclopedia: Computability theory |
| | 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. | | | Computability logic is a formal theory of computability, introduced by Giorgi Japaridze in 2003. | | | Electronic computers, and even quantum computers, are exactly equivalent to Turing machines, if they have access to an unbounded supply of memory. |
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http://www.nationmaster.com/encyclopedia/Computability-theory
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| | Computational complexity theory - Wikipedia, the free encyclopedia |
| | In computer science, computational complexity theory is the branch of the theory of computation that studies the resources, or cost, of the computation required to solve a given problem. | | | After the theory explaining which problems can be solved and which cannot be, it was natural to ask about the relative computational difficulty of computable functions. | | | Complexity theory differs from computability theory, which deals with whether a problem can be solved at all, regardless of the resources required. |
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http://en.wikipedia.org/wiki/Computational_complexity_theory
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| | Computing with Reals - some history |
| | Recursion theory provides a basis for an understanding of computability separated from too great an exposure to philosophy. | | | For many years after Turing's first papers recursion theory was concerned primarily with computation over the natural numbers and little work was done on computation over reals. | | | To those of us who were born after the invention of the digital computer, who learned about recursion theory in our youths, (perhaps even those who escaped the recursion theory, but couldn't escape computers), the writings of intuitionist may appear unnecessarily obscure. |
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http://www.rbjones.com/rbjpub/cs/cs006.htm
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| | Publisher description for Library of Congress control number 79051823 |
| | This book is an introduction to computability theory (or recursion theory as it is traditionally known to mathematicians). | | | The later chapters provide an introduction to more advanced topics such as Gildel's incompleteness theorem, degrees of unsolvability, the Recursion theorems and the theory of complexity of computation. | | | Dr Cutland begins with a mathematical characterisation of computable functions using a simple idealised computer (a register machine); after some comparison with other characterisations, he develops the mathematical theory, including a full discussion of non-computability and undecidability, and the theory of recursive and recursively enumerable sets. |
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http://www.loc.gov/catdir/description/cam022/79051823.html
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| | Syllabus |
| | This course focuses on the traditional, algorithmic theory of computation consisting of three subareas: (1) computability, (2) complexity theory, and (3) formal languages and automata. | | | Interactive computation subsumes algorithmic computation, but not vice versa. | | | Computational problems can be represented as a set, readily available as the input to computational processing. |
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http://www.tcnj.edu/~komagata/csc460/05s/syllabus-460-05s.php
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| | Luciano Floridi |
| | Alan Turing's contributions to computer science are so outstanding that two of his seminal papers, "On Computable Numbers with an application to the Entscheidungsproblem" and "Computing Machinery and Intelligence", have provided the foundations for the development of the theory of computability, recursion functions and artificial intelligence. | | | Typical cases of computational procedures satisfying the algorithmic criterion are provided by truth tables and tableaux in propositional logic, and the elementary operations in arithmetic, such as the multiplication of two integers. | | | U) a UTM can compute anything a computer can compute. |
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http://www.wolfson.ox.ac.uk/~floridi/ctt.htm
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| | Complexity Theory 2004/5 Moni Naor |
| | Michael Sipser, Introduction to the Theory of Computation, 1997 | | | Lecturers: Steven Rudich and Avrim Blum, Computational Complexity Theory, University: CMU. | | | PREREQUISITES: Students are expected to be familiar with algorithms, data structures, probability theory, and linear algebra, at an undergraduate level; a basic course in computability is assumed. |
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http://www.wisdom.weizmann.ac.il/~naor/COURSE/complexity.html
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| | Computational Complexity Theory (ResearchIndex) |
| | By quantifying these resources, complexity theory has profoundly affected our thinking about computation. | | | @article{ loui96computational, author = "Michael C. Loui", title = "Computational complexity theory", journal = "ACM Computing Surveys", volume = "28", number= "1", pages = "47--49", year = "1996", url = "citeseer.ist.psu.edu/loui96computational.html" } | | | Computability theory establishes the existence of undecidable problems that cannot be solved in principle, regardless of the amount of time invested. |
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http://citeseer.ist.psu.edu/500303.html
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| | Field Computation Bibliography |
| | The theory treats computations as continuous transformations of fields which are continuous assemblies of continuous values data. | | | Pour-El, M. Abstract Computability and its Relation to the General Purpose Analog Computer. | | | This paper proves a particular field computer (a spatial continuum-limit neural net) governed by a purely linear integro-differential equation is computationally universal. |
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http://www.cs.utk.edu/~mclennan/fieldcomp-biblio.html
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| | AIT05 mainpage |
| | Algorithmic Information Theory is an international meeting bringing together mathematicians, computer theorists, logicians, mathematical physicists and scientists in related fields to assess the impact of recent development in the foundations of mathematics, computability, computation and computer- | | | Welcome to the Algorithmic Information Theory Conference in Vaasa 16th-18th May 2005 | | | supported mathematical theory exploration, and to stimulate further research in these and related fields. |
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http://www.uwasa.fi/ait05
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| | CS403 - Computational Complexity Theory |
| | Q3 Which of the following models of computation is more powerful (in terms of computability) than the others? | | | Q6 The computational complexity class PTIME, often referred to as P,... | | | (a) defines a lower bound on the complexity of Turing machines deciding these languages |
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http://www.cs.may.ie/~tnaughton/teaching/cs403_old/cs4032000test02repeat.html
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| | Computability theory Did You Mean Recursion theory |
| | Computability theory is the branch of theoretical computer science that studies which problems are computationally solvable using different models of computation. | | | This work is licensed under a Creative Commons License. | | | Visit partners of Did you mean Travel: Partners |
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http://www.did-you-mean.com/Recursion_theory.html
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| | Computability logic - encyclopedia article about Computability logic. |
| | in 2003, Computability logic is a research programme and mathematical framework for redeveloping logic as a systematic formal theory of computability, as opposed to classical logic Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. | | | Defining what such game-playing machines mean, computability logic provides a generalization of the Church-Turing thesis In computability theory the Church-Turing thesis, Church's thesis, Church's conjecture or Turing's thesis, named after Alonzo Church and Alan Turing, is a hypothesis about the nature of mechanical calculation devices, such as electronic computers. | | | Being semantically constructed, as yet computability logic does not have a fully developed proof theory. |
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http://encyclopedia.thefreedictionary.com/Computability+logic
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| | CCA Net - Conference CCA 2004 |
| | Scientists working in the area of computation on real-valued data come from different fields, such as theoretical computer science, domain theory, logic, constructive mathematics, computer arithmetic, numerical mathematics, analysis, etc. | | | Unlike the well established classical theory of computation over discrete structures, the theory of computation over continuous data is still in its infancy. | | | Computability theory and complexity theory are two central areas of research in mathematical logic and theoretical computer science. |
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http://cca-net.de/cca2004
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| | 11: Number theory |
| | See also section 11Y: Computational number theory for issues regarding the current limits of computability in number theory (especially regarding factorizations and primality testing). | | | "Computational number theory" studies the effectiveness of algorithms for computation of number-theoretic quantities. | | | KANT, a system for "Computational Algebraic Number Theory" |
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http://www.math.niu.edu/~rusin/known-math/index/11-XX.html
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| | Powell's Books - Computability and Complexity Theory (01 Edition) by Steven Homer and Alan L. Selman |
| | 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. | | | This comprehensive introduction begins with classical computability theory and develops complexity theory on top of that. | | | The theory of computing provides computer science with concepts, models, and formalism for reasoning about the resources needed to carry out computations, and the efficiency of the computations. |
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http://www.powells.com/cgi-bin/biblio?inkey=65-0387950559-1
(275 words)
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| | Hypercomputation: Encyclopedia topic |
| | The field known as computability theory (computability theory: computability theory is that part of the theory of computation dealing with which problems... | | | General development of complexity theory for abstract machines that compute on real or complex numbers instead of bits. | | | Hypercomputation refers to methods for the computation of non-computable function (non-computable function: generally a computable function is a partial function... |
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http://www.absoluteastronomy.com/reference/hypercomputation
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| | Ugesedler |
| | Michael Sipser: "Introduction to the Theory of Computation", PWS (1996). | | | This question reveals that Computability, other than in Complexity Theory, releases any kind of restriction on resources such as running time or memory consumption; and nevertheless, some important problems are still provably uncomputable as Alan Turing revealed (any student of Computer Science should be able to name such a problem)! | | | We extend his theory from single reals to vectors, to functions, and to sets, and we compare it to other new theories of computability. |
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http://www.imada.sdu.dk/~ziegler/advcomp
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| | Computability logic |
| | Computability logic is an attempt to lay foundations for a comprehensive and systematic theory of interactive computation. | | | Computability logic is a conservative extension of classical logic and, being more expressive, constructive and computationally meaningful, it has a wide range of application areas. | | | Computability logic is a formal theory of computability, introduced by Japaridze in 2003. |
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http://www.nebulasearch.com/encyclopedia/article/Computability_logic.html
(496 words)
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| | Computational complexity theory |
| | Complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. | | | Complexity theory differs from computability theory, which deals with whether a problem can be solved at all, regardless of the resources required. | | | After the theory explaining which problems can be solved and which cannot be, it was natural to ask about the relative computational difficulty of computable functions. |
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http://hallencyclopedia.com/Computational_complexity_theory
(1159 words)
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| | CS520: An Introduction to the Theory of Computation |
| | We will study automata theory, formal languages, the theory of computability and undecidability, and computational complexity. | | | This will be perhaps the first course in which the student is exposed to the rigorous treatment of the fundamental theory of computability and complexity. | | | This course is an introduction to the theory of computation. |
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http://www.cs.wisc.edu/~jyc/cs520.html
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