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# Topic: Theory of computation

###### In the News (Thu 18 Apr 19)

 Theory of computation - Wikipedia, the free encyclopedia Computability theory deals primarily with the question of whether a problem is solvable at all on a computer. The halting problem is one of the most important results in computability theory, as it is an example of a concrete problem that is both easy to formulate and impossible to solve using a Turing machine. 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. en.wikipedia.org /wiki/Theory_of_computation   (1029 words)

 Computation - Wikipedia, the free encyclopedia However, the meaning of the word "computer" should be understood here in a large sense, since it does not apply only to digital computers. In computer science (which is sometimes described as the discipline that studies computations) and in mathematical logic, 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   (238 words)

 Theory and Algorithms Research Theory of computation gives a way to exploit tractability via a choice of several powerful algorithmic techniques. theory group at Microsoft Research is an invaluable resource -- on top of research collaborations, we benefit from their innumerable seminars and the advanced theory courses their members often offer at UW. Computational Biology This project addresses a wide variety of algorithmic problems related to mapping and sequencing of genomes, discovery of significant signals in DNA and protein sequences, design of DNA microarrays, analysis of expression data, and neurally inspired computing. www.cs.washington.edu /research/computation   (627 words)

 PRONUNCIATION   (Site not responding. Last check: 2007-09-20) The theory of computation is the study of mathematical models of computing, independent of any particular computer hardware. At that time, mathematicians were trying to design a computing machine that would automate the process of computing, in much the same way that the machines of the Industrial Revolution had automated many agricultural and manufacturing processes. An essential step in automating computing is deciding what steps are involved in computing: that is, what kind of memory is available (e.g., a single string, a fixed number of registers storing numbers, or an infinitely long tape storing characters), and what kinds of computational steps can be performed on the data in memory. nupedia.8media.org /nupedia/article/short/The+Theory+of+Computation   (464 words)

 Theory of Computation 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)

 Theory Group The theory group brings together researchers in many areas of mathematics and physics to develop novel approaches to problems in computer science and information technology. Among the areas of expertise we have are statistical physics, probability theory, combinatorics, geometry and topology, theoretical computer science, and algorithms. We are also developing topological error correcting codes for quantum computation, and studying the relationship of quantum computation to topological quantum field theory. research.microsoft.com /theory   (462 words)

 Theory of Computation at Harvard Faculty and students in the Theory of Computation group aim to Apply this understanding to address problems arising in other parts of computer science and mathematics, and in other fields such as neuroscience and physics. Theory Group Postdocs: Occasionally, we have postdoc positions available. www.eecs.harvard.edu /theory   (138 words)

 Theory of Computation Theory of computing is the fundamental scientific discipline concerned with understanding (efficient) computational phenomena, whether it be man-made, in nature, or imaginary. Physical machines seem complicated and therefore difficult to analyze, but the mere fact that we build and use them gives some indication that we might actually be able to understand their essential characteristics. 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. www.cs.princeton.edu /introcs/70theory   (272 words)

 Amazon.com: Introduction to the Theory of Computation: Books: Michael Sipser   (Site not responding. Last check: 2007-09-20) Introduction to Computer Theory by Daniel I. Cohen The field is divided into two major branches: computability theory and complexity theory, but both branches deal with formal models of computation, and both of these subjects are dealt with in this book. It discusses the idea that even though a problem may be computable in principle, it may not be solvable in practice due to the time required. www.amazon.com /exec/obidos/tg/detail/-/053494728X?v=glance   (2402 words)

 Theory of Computation Like a finite automaton, a Turing machine is a simple computing device consisting of a finite set of input states, finite set of input symbols, an initial state, and a transition function. When we say a computational device is universal, we typically mean that the device has the capability to simulate any other computational device. For example, if you were to show a system capable of simulating the components necessary and sufficient to build a computer (gates, timers, etc.) then you would have shown that system to be a universal computer. www.theory.org /complexity/cdpt/html/node3.html   (1966 words)

 Conclusion: Mathematical Theory of Computation   (Site not responding. Last check: 2007-09-20) 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. 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. 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. www-formal.stanford.edu /jmc/basis1/node15.html   (133 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)

 Computation Theory The aim of this course is to introduce several apparently different formalisations of the informal notion of algorithm; to show that they are equivalent; and to use them to demonstrate that there are uncomputable functions and algorithmically undecidable problems. Computing partial recursive functions on a register machine. Brookshear, J.G. Theory of computation: formal languages, automata, and complexity. www.cl.cam.ac.uk /DeptInfo/CST03/node45.html   (347 words)

 CECS 341 Theory of Computation We study both the inherent capabilities and limitations of these computational models as well as their relationships with formal languages. Introduction to the Theory of Computation, by Michael Sipser, PWS publishing Co., 1997. Hopcroft and Ullman, Introduction to automata theory, languages, and computation, by Hopcroft and Ullman, Addison-Wesley, 1979. meru.cecs.missouri.edu /courses/cecs341/tc.html   (375 words)

 Workshop on Proof Theory and Computation The focus of the workshop is on proof theory and computation: we aim at a small, informal event where people have plenty of time to exchange ideas. By applying insights from proof theory and the philosophy of language, the theory of harmony in logic and type theory hopes to provide a more natural approach than either denotational or operational approaches. This workshop is organized by the AI Institute at TU Dresden, and sponsored by IQN (Rational mobile agents and systems of agents) and Graduiertenkolleg 334 (Specification of discrete processes and systems of processes by operational models and logics). www.ki.inf.tu-dresden.de /~guglielm/WPT   (1217 words)

 [No title] During this past decade the theory of formation of singularities was developed for Ricci flow and mean curvature flow, which has had a large impact on other geometric flows. The recent theoretical progress on geometric flows, especially on understanding weak solutions and singularities, together with the recent computational progress on geometric flows makes this an opportune time to hold a workshop which will bring together mathematicians working on the theoretical and numerical aspects of geometric flows. Numerical computation of moving interfaces and geometric flows is quite challenging due to dynamic deformation of geometry, nonlinearity and possible development of singularities, especially topological changes. www.ipam.ucla.edu /programs/gf2004   (715 words)

 UofT DCS Theory of Computation Research Group Info In the theory of computation area, we use mathematical techniques to understand the nature of computation and to design and analyze algorithms for important and fundamental problems. The members of the complexity theory group are all interested, in one way or another, in the limitations of computation: What problems are not feasible to solve on a computer? Theoretical computer science provides important new ways of thinking about computation and provides lasting insights that are applicable to a wide variety of systems. www.cs.toronto.edu /DCS/Research/theory.html   (205 words)

 Theory of Computation A theoretical treatment of what can be computed and how fast it can be done. Text: Introduction to the Theory of Computation, Michael Sipser. Reference: Introduction to Automata Theory, Languages and Computation, Hopcroft, Motwani and Ullman. aduni.org /courses/theory   (102 words)

 Theory of Computation   (Site not responding. Last check: 2007-09-20) 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. www.cs.umass.edu /~immerman/cs601   (335 words)

 Theory of Computation GAP (Groups, Algorithms and Programming) is a system for computational discrete algebra with particular emphasis on, but not restricted to computational group theory. Following the retirement of J. Neubueser from the chair of LDFM, the development and maintenance of GAP is coordinated by the School of Computer Science at the University of St Andrews, Scotland. The aim of the Intelligent Computation Group at St Andrews is to provide effective computation through modelling of both biological and cognitive insights into intelligent information processing and representation. www.dcs.st-and.ac.uk /research/theory   (269 words)

 ETH - InfSec - Lecture: Theory of Computation (251-0006-00) Theory extracts the basic concepts that apply to any conceivable implementation of computing machines. H.R. Lewis, C.H. Papadimitriou: Elements of the theory of computation, Prentice-Hall, 1981 M. Sipser: Introduction to the theory of computation, PWS Publ. www.infsec.ethz.ch /education/ss04/theoinf   (518 words)

 Plasma Theory and Computation Research in Nuclear Engineering   (Site not responding. Last check: 2007-09-20) Plasma theory research is carried out as an interdepartmental activity organized under the Center for Plasma Theory and Computation. EP faculty and staff involved in the center are Professors Callen, Emmert and Moses, and scientists Hegna, Litwin and Santarius. Also participating in the center are Professors Scharer and Tataronis (electrical and computer engineering), and Professors Prager and Terry (physics). www.engr.wisc.edu /ep/neep/research/cptc.html   (170 words)

 Theory of Computation at Columbia Computational Complexity: Galil, Grunschlag, Malkin, Servedio, Traub, Werschulz, Wozniakowski, Yannakakis, Yung Quantum Computation: Aho, Papageorgiou, Servedio, Traub, Werschulz, Wozniakowski Columbia Theory Seminar, past semesters: Fall 2005 Spring 2005, Fall 2004, Spring 2004, Fall 2003, Spring 2003 www.cs.columbia.edu /theory   (156 words)

 Theory and computation of spheroidal wavefunctions In this paper we report on a package, written in the Mathematica computer algebra system, which has been developed to compute the spheroidal wavefunctions of Meixner and Schäfke (1954 Mathieusche Funktionen und Sphäroidfunktionen) and is available online (physics.uwa.edu.au/~falloon/spheroidal/spheroidal.html). This package represents a substantial contribution to the existing software, since it computes the spheroidal wavefunctions to arbitrary precision for general complex parameters μ, ν, γ and argument z; existing software can only handle integer μ, ν and does not give arbitrary precision. This paper presents a concise review of the general theory of spheroidal wavefunctions and a description of the formulae and algorithms used in their computation, and gives high precision numerical examples. stacks.iop.org /0305-4470/36/5477   (308 words)

 Introduction to Automata Theory, Languages, and Computation   (Site not responding. Last check: 2007-09-20) A completely revised edition of the Hopcroft-Ullman automata book from 1979 (Addison-Wesley) was published in November, 2000. The revised edition features more explanations and intuition, more applications, and a selection of topics with an eye toward balancing the need for relevance with the need to master the foundations of computer science. This service lets students work conventional problems in automata and langauage theory, and tests their knowledge by random sampling of their work --- via multiple choice. www-db.stanford.edu /~ullman/ialc.html#slides   (249 words)

 A BASIS FOR A MATHEMATICAL THEORY OF COMPUTATION   (Site not responding. Last check: 2007-09-20) A BASIS FOR A MATHEMATICAL THEORY OF COMPUTATION An earlier version was published in 1961 in the Proceedings of the Western Joint Computer Conference. On the Relations between Computation and Mathematical Logic www-formal.stanford.edu /jmc/basis1/basis1.html   (78 words)

 Bibliographies on Theory/Foundations of Computer Science   (Site not responding. Last check: 2007-09-20) A large bibliography on theory/foundations of computer science Bibliography of the proceedings volumes of the annual ACM Symposia on the Theory of Computing (STOC) Bibliography of the proceedings of the annual IEEE symposia on the Foundations of Computer Science (FOCS) liinwww.ira.uka.de /bibliography/Theory   (346 words)

 Home Page for Math 485 Textbook: Introduction to Languages and Theory of Computation, Second edition Introduction to the Theory of Computation by Michael Sipser -- pub.PWS Publishing Co. Introduction to Automata Theory, Languages and Computation by J. Hopcroft and J. Ullman -- pub. Addison Wesley The Theory of Parsing, Translation and Compiling, Volume I: Parsing by A.V. Aho and J. Ullman -- pub. www.webpages.uidaho.edu /~ebarbut/m485.html   (179 words)

 Stanford CS Theory   (Site not responding. Last check: 2007-09-20) As theoretical computer scientists, we seek greater understanding of fundamental computational techniques and their inherent limitations. Research includes the development of new sequential and parallel algorithms, computational problems in databases, computational geometry, design and analysis of programs and programming languages, and supporting studies in combinatorial, logical, and algebraic mathematics. Administrative life of the Theory student -- quals, thesis info, etc. theory.stanford.edu   (81 words)

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