Download or read book Degrees of Unsolvability and Relative Computability of Real Numbers written by Anthony James Dunlop and published by . This book was released on 1999 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computability and Complexity in Analysis written by Jens Blanck and published by Springer. This book was released on 2003-06-29 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: The workshop on Computability and Complexity in Analysis, CCA 2000, was hosted by the Department of Computer Science of the University of Wales Swansea, September 17{19, 2000. It was the fourth workshop in a successful series of workshops: CCA’95 in Hagen, Germany, CCA’96 in Trier, Germany, and CCA’98 in Brno, Czech Republic. About 40 participants from the countries United Kingdom, Germany, Japan, Italy, Russia, France, Denmark, Greece, and Ireland contributed to the success of this meeting. Altogether, 28 talkswere p- sented in Swansea. These proceedings include 23 papers which represent a cro- section through recent research on computability and complexity in analysis. The workshop succeeded in bringing together people interested in computability and complexity aspects of analysis and in exploring connections with nume- cal methods, physics and, of course, computer science. It was rounded o by a number of talks and papers on exact computer arithmetic and by a competition of v e implemented systems. A report on this competition has been included in these proceedings. We would like to thank the authors for their contributions and the referees for their careful work, and we hope for further inspiring and constructive meetings of the same kind. April 2001 Jens Blanck Vasco Brattka Peter Hertling Organization CCA2000was hosted by the Department of Computer Science of the University of Wales Swansea and took place on September 17{19, 2000.
Download or read book Mathematical Foundations of Computer Science 1999 written by Miroslaw Kutylowski and published by Springer. This book was released on 2007-07-16 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers selected for presentation during the 24th Interna tional Symposium on Mathematical Foundations of Computer Science held on September 6-10, 1999 in Szklarska Por^ba, Poland. The symposium, organized alternately in the Czech Republic, Slovakia, and Poland, focuses on theoretical aspects and mathematical foundations of computer science. The scientific program of the symposium consists of five invited talks given by Martin Dyer, Dexter Kozen, Giovanni Manzini, Sergio Rajsbaum, and Mads Tofte, and 37 accepted papers chosen out of 68 submissions. The volume contains all accepted contributed papers, and three invited papers. The contributed papers have been selected for presentation based on their scientific quality, novelty, and interest for the general audience of MFCS par ticipants. Each paper has been reviewed by at least three independent referees — PC members and/or sub-referees appointed by them. The papers were se lected for presentation during a fully electronic virtual meeting of the program committee on May 7, 1999. The virtual PC meeting was supported by software written by Artur Zgoda, Ph.D. student at the University of Wroclaw. The entire communication and access to quite a sensitive database at PC headquarters in Wroclaw was secured by cryptographic protocols based on technology of certificates.
Download or read book Causality Meaningful Complexity and Embodied Cognition written by A. Carsetti and published by Springer Science & Business Media. This book was released on 2010-03-10 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arturo Carsetti According to molecular Biology, true invariance (life) can exist only within the framework of ongoing autonomous morphogenesis and vice versa. With respect to this secret dialectics, life and cognition appear as indissolubly interlinked. In this sense, for instance, the inner articulation of conceptual spaces appears to be linked to an inner functional development based on a continuous activity of selection and “anchorage” realised on semantic grounds. It is the work of “invention” and g- eration (in invariance), linked with the “rooting” of meaning, which determines the evolution, the leaps and punctuated equilibria, the conditions related to the unfo- ing of new modalities of invariance, an invariance which is never simple repetition and which springs on each occasion through deep-level processes of renewal and recovery. The selection perpetrated by meaning reveals its autonomy aboveall in its underpinning, in an objective way, the ongoing choice of these new modalities. As such it is not, then, concerned only with the game of “possibles”, offering itself as a simple channel for pure chance, but with providing a channel for the articulation of the “ le” in the humus of a semantic (and embodied) net in order to prepare the necessary conditionsfor a continuousrenewal and recoveryof original creativity. In effect, it is this autonomy in inventing new possible modules of incompressibility whichdeterminestheactualemergenceofnew(andtrue)creativity,whichalsotakes place through the “narration” of the effected construction.
Download or read book Computability written by Douglas S. Bridges and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at mathematicians and computer scientists who will only be exposed to one course in this area, Computability: A Mathematical Sketchbook provides a brief but rigorous introduction to the abstract theory of computation, sometimes also referred to as recursion theory. It develops major themes in computability theory, such as Rice's theorem and the recursion theorem, and provides a systematic account of Blum's complexity theory as well as an introduction to the theory of computable real numbers and functions. The book is intended as a university text, but it may also be used for self-study; appropriate exercises and solutions are included.
Download or read book Alan Turing written by S. Barry Cooper and published by Elsevier. This book was released on 2013-03-18 with total page 937 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this 2013 winner of the prestigious R.R. Hawkins Award from the Association of American Publishers, as well as the 2013 PROSE Awards for Mathematics and Best in Physical Sciences & Mathematics, also from the AAP, readers will find many of the most significant contributions from the four-volume set of the Collected Works of A. M. Turing. These contributions, together with commentaries from current experts in a wide spectrum of fields and backgrounds, provide insight on the significance and contemporary impact of Alan Turing's work. Offering a more modern perspective than anything currently available, Alan Turing: His Work and Impact gives wide coverage of the many ways in which Turing's scientific endeavors have impacted current research and understanding of the world. His pivotal writings on subjects including computing, artificial intelligence, cryptography, morphogenesis, and more display continued relevance and insight into today's scientific and technological landscape. This collection provides a great service to researchers, but is also an approachable entry point for readers with limited training in the science, but an urge to learn more about the details of Turing's work. - 2013 winner of the prestigious R.R. Hawkins Award from the Association of American Publishers, as well as the 2013 PROSE Awards for Mathematics and Best in Physical Sciences & Mathematics, also from the AAP - Named a 2013 Notable Computer Book in Computing Milieux by Computing Reviews - Affordable, key collection of the most significant papers by A.M. Turing - Commentary explaining the significance of each seminal paper by preeminent leaders in the field - Additional resources available online
Download or read book New Computational Paradigms written by Barry S. Cooper and published by Springer Science & Business Media. This book was released on 2005-05-23 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the first International Conference on Computability in Europe, CiE 2005, held in Amsterdam, The Netherlands in June 2005. The 68 revised full papers presented were carefully reviewed and selected from 144 submissions. Among them are papers corresponding to two tutorials, six plenary talks and papers of six special sessions involving mathematical logic and computer science at the same time as offering the methodological foundations for models of computation. The papers address many aspects of computability in Europe with a special focus on new computational paradigms. These include first of all connections between computation and physical systems (e.g., quantum and analog computation, neural nets, molecular computation), but also cover new perspectives on models of computation arising from basic research in mathematical logic and theoretical computer science.
Download or read book Computation and Logic in the Real World written by S. Barry Cooper and published by Springer Science & Business Media. This book was released on 2007-06-11 with total page 842 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Conference on Computability in Europe, CiE 2007, held in Sienna, Italy, in June 2007. The 50 revised full papers presented together with 36 invited papers were carefully reviewed and selected from 167 submissions.
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2000 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Turing Computability written by Robert I. Soare and published by Springer. This book was released on 2016-06-20 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Turing's famous 1936 paper introduced a formal definition of a computing machine, a Turing machine. This model led to both the development of actual computers and to computability theory, the study of what machines can and cannot compute. This book presents classical computability theory from Turing and Post to current results and methods, and their use in studying the information content of algebraic structures, models, and their relation to Peano arithmetic. The author presents the subject as an art to be practiced, and an art in the aesthetic sense of inherent beauty which all mathematicians recognize in their subject. Part I gives a thorough development of the foundations of computability, from the definition of Turing machines up to finite injury priority arguments. Key topics include relative computability, and computably enumerable sets, those which can be effectively listed but not necessarily effectively decided, such as the theorems of Peano arithmetic. Part II includes the study of computably open and closed sets of reals and basis and nonbasis theorems for effectively closed sets. Part III covers minimal Turing degrees. Part IV is an introduction to games and their use in proving theorems. Finally, Part V offers a short history of computability theory. The author has honed the content over decades according to feedback from students, lecturers, and researchers around the world. Most chapters include exercises, and the material is carefully structured according to importance and difficulty. The book is suitable for advanced undergraduate and graduate students in computer science and mathematics and researchers engaged with computability and mathematical logic.
Download or read book Logical Approaches to Computational Barriers written by Arnold Beckmann and published by Springer. This book was released on 2006-06-29 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second International Conference on Computability in Europe, CiE 2006, held in Swansea, UK, June/July 2006. The book presents 31 revised full papers together with 30 invited papers, including papers corresponding to 8 plenary talks and 6 special sessions on proofs and computation, computable analysis, challenges in complexity, foundations of programming, mathematical models of computers and hypercomputers, and Gödel centenary: Gödel's legacy for computability.
Download or read book Computable Structure Theory written by Antonio Montalbán and published by Cambridge University Press. This book was released on 2021-06-24 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: In mathematics, we know there are some concepts - objects, constructions, structures, proofs - that are more complex and difficult to describe than others. Computable structure theory quantifies and studies the complexity of mathematical structures, structures such as graphs, groups, and orderings. Written by a contemporary expert in the subject, this is the first full monograph on computable structure theory in 20 years. Aimed at graduate students and researchers in mathematical logic, it brings new results of the author together with many older results that were previously scattered across the literature and presents them all in a coherent framework, making it easier for the reader to learn the main results and techniques in the area for application in their own research. This volume focuses on countable structures whose complexity can be measured within arithmetic; a forthcoming second volume will study structures beyond arithmetic.
Download or read book Computability and Complexity written by Adam Day and published by Springer. This book was released on 2016-11-30 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift is published in honor of Rodney G. Downey, eminent logician and computer scientist, surfer and Scottish country dancer, on the occasion of his 60th birthday. The Festschrift contains papers and laudations that showcase the broad and important scientific, leadership and mentoring contributions made by Rod during his distinguished career. The volume contains 42 papers presenting original unpublished research, or expository and survey results in Turing degrees, computably enumerable sets, computable algebra, computable model theory, algorithmic randomness, reverse mathematics, and parameterized complexity, all areas in which Rod Downey has had significant interests and influence. The volume contains several surveys that make the various areas accessible to non-specialists while also including some proofs that illustrate the flavor of the fields.
Download or read book Slicing The Truth On The Computable And Reverse Mathematics Of Combinatorial Principles written by Denis R Hirschfeldt and published by World Scientific. This book was released on 2014-07-18 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a case-study approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions.
Download or read book Computing Nature written by Gordana Dodig-Crnkovic and published by Springer Science & Business Media. This book was released on 2013-03-21 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about nature considered as the totality of physical existence, the universe, and our present day attempts to understand it. If we see the universe as a network of networks of computational processes at many different levels of organization, what can we learn about physics, biology, cognition, social systems, and ecology expressed through interacting networks of elementary particles, atoms, molecules, cells, (and especially neurons when it comes to understanding of cognition and intelligence), organs, organisms and their ecologies? Regarding our computational models of natural phenomena Feynman famously wondered: “Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?” Phenomena themselves occur so quickly and automatically in nature. Can we learn how to harness nature’s computational power as we harness its energy and materials? This volume includes a selection of contributions from the Symposium on Natural Computing/Unconventional Computing and Its Philosophical Significance, organized during the AISB/IACAP World Congress 2012, held in Birmingham, UK, on July 2-6, on the occasion of the centenary of Alan Turing’s birth. In this book, leading researchers investigated questions of computing nature by exploring various facets of computation as we find it in nature: relationships between different levels of computation, cognition with learning and intelligence, mathematical background, relationships to classical Turing computation and Turing’s ideas about computing nature - unorganized machines and morphogenesis. It addresses questions of information, representation and computation, interaction as communication, concurrency and agent models; in short this book presents natural computing and unconventional computing as extension of the idea of computation as symbol manipulation.
Download or read book Handbook of Computability Theory written by E.R. Griffor and published by Elsevier. This book was released on 1999-10-01 with total page 741 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters of this volume all have their own level of presentation. The topics have been chosen based on the active research interest associated with them. Since the interest in some topics is older than that in others, some presentations contain fundamental definitions and basic results while others relate very little of the elementary theory behind them and aim directly toward an exposition of advanced results. Presentations of the latter sort are in some cases restricted to a short survey of recent results (due to the complexity of the methods and proofs themselves). Hence the variation in level of presentation from chapter to chapter only reflects the conceptual situation itself. One example of this is the collective efforts to develop an acceptable theory of computation on the real numbers. The last two decades has seen at least two new definitions of effective operations on the real numbers.
Download or read book L2 Invariants Theory and Applications to Geometry and K Theory written by Wolfgang Lück and published by Springer Science & Business Media. This book was released on 2002-08-06 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.
