The Computability Of The World
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Turing Computability
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Author : Robert I. Soare
language : en
Publisher: Springer
Release Date : 2016-06-20
Turing Computability written by Robert I. Soare and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-20 with Computers categories.
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.
Computability In Context Computation And Logic In The Real World
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Author : S Barry Cooper
language : en
Publisher: World Scientific
Release Date : 2011-02-25
Computability In Context Computation And Logic In The Real World written by S Barry Cooper and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-25 with Mathematics categories.
Computability has played a crucial role in mathematics and computer science, leading to the discovery, understanding and classification of decidable/undecidable problems, paving the way for the modern computer era, and affecting deeply our view of the world. Recent new paradigms of computation, based on biological and physical models, address in a radically new way questions of efficiency and challenge assumptions about the so-called Turing barrier.This volume addresses various aspects of the ways computability and theoretical computer science enable scientists and philosophers to deal with mathematical and real-world issues, covering problems related to logic, mathematics, physical processes, real computation and learning theory. At the same time it will focus on different ways in which computability emerges from the real world, and how this affects our way of thinking about everyday computational issues./a
The Computability Of The World
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Author : Bernd-Olaf Küppers
language : en
Publisher: Springer
Release Date : 2017-11-28
The Computability Of The World written by Bernd-Olaf Küppers and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-28 with Science categories.
In this thought-provoking book Küppers, an internationally renowned physicist, philosopher and theoretical biologist, addresses a number of science's deepest questions: Can physics advance to the origin of all things and explain the unique phenomena of life, time and history? Are there unsolvable enigmas of the world? How did life originate? Is language a general phenomenon of Nature? What is time? Is it possible to express the history of the world in formulae? Where is science leading us? These and other provocative questions essential for a deeper understanding of the world are treated here in a refreshing and stimulating manner.
Computation And Logic In The Real World
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Author : S. Barry Cooper
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-11
Computation And Logic In The Real World written by S. Barry Cooper and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-11 with Computers categories.
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.
Computability
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Author : B. Jack Copeland
language : en
Publisher: MIT Press
Release Date : 2013-06-07
Computability written by B. Jack Copeland and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-07 with Computers categories.
Computer scientists, mathematicians, and philosophers discuss the conceptual foundations of the notion of computability as well as recent theoretical developments. In the 1930s a series of seminal works published by Alan Turing, Kurt Gödel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics. In the decades since, the theory of computability has moved to the center of discussions in philosophy, computer science, and cognitive science. In this volume, distinguished computer scientists, mathematicians, logicians, and philosophers consider the conceptual foundations of computability in light of our modern understanding.Some chapters focus on the pioneering work by Turing, Gödel, and Church, including the Church-Turing thesis and Gödel's response to Church's and Turing's proposals. Other chapters cover more recent technical developments, including computability over the reals, Gödel's influence on mathematical logic and on recursion theory and the impact of work by Turing and Emil Post on our theoretical understanding of online and interactive computing; and others relate computability and complexity to issues in the philosophy of mind, the philosophy of science, and the philosophy of mathematics.ContributorsScott Aaronson, Dorit Aharonov, B. Jack Copeland, Martin Davis, Solomon Feferman, Saul Kripke, Carl J. Posy, Hilary Putnam, Oron Shagrir, Stewart Shapiro, Wilfried Sieg, Robert I. Soare, Umesh V. Vazirani
A Computable Universe
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Author : Hector Zenil
language : en
Publisher: World Scientific
Release Date : 2013
A Computable Universe written by Hector Zenil and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Computers categories.
This volume discusses the foundations of computation in relation to nature. It focuses on two main questions: What is computation? and How does nature compute?
Sailing Routes In The World Of Computation
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Author : Florin Manea
language : en
Publisher: Springer
Release Date : 2018-07-23
Sailing Routes In The World Of Computation written by Florin Manea and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-23 with Computers categories.
This book constitutes the refereed proceedings of the 14th Conference on Computability in Europe, CiE 2018, held in Kiel, Germany, in July/ August 2017. The 26 revised full papers were carefully reviewed and selected from 55 submissions. In addition, this volume includes 15 invited papers. The conference CiE 2018 has six special sessions, namely: Approximation and optimization, Bioinformatics and bio-inspired computing, computing with imperfect information, continuous computation, history and philosophy of computing (celebrating the 80th birthday of Martin Davis), and SAT-solving.
Physics And Our View Of The World
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Author : Jan Hilgevoord
language : en
Publisher: Cambridge University Press
Release Date : 1994-11-03
Physics And Our View Of The World written by Jan Hilgevoord and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-11-03 with Religion categories.
An examination of the claims of modern physics, and their impact on our view of the world.
Computability And Models
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Author : Barry S. Cooper
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computability And Models written by Barry S. Cooper and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Science involves descriptions of the world we live in. It also depends on nature exhibiting what we can best describe as a high aLgorithmic content. The theme running through this collection of papers is that of the interaction between descriptions, in the form of formal theories, and the algorithmic content of what is described, namely of the modeLs of those theories. This appears most explicitly here in a number of valuable, and substantial, contributions to what has until recently been known as 'recursive model theory' - an area in which researchers from the former Soviet Union (in particular Novosibirsk) have been pre-eminent. There are also articles concerned with the computability of aspects of familiar mathematical structures, and - a return to the sort of basic underlying questions considered by Alan Turing in the early days of the subject - an article giving a new perspective on computability in the real world. And, of course, there are also articles concerned with the classical theory of computability, including the first widely available survey of work on quasi-reducibility. The contributors, all internationally recognised experts in their fields, have been associated with the three-year INTAS-RFBR Research Project "Com putability and Models" (Project No. 972-139), and most have participated in one or more of the various international workshops (in Novosibirsk, Heidelberg and Almaty) and otherresearch activities of the network.
Computability Theory
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Author : S. Barry Cooper
language : en
Publisher: CRC Press
Release Date : 2017-09-06
Computability Theory written by S. Barry Cooper and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-06 with Mathematics categories.
Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. 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. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences. Written by a leading researcher, Computability Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The book includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable and lively way.