Computability In Context: Computation And Logic In The Real World
Computability In Context: Computation And Logic In The Real World

Author: S Barry Cooper

Publisher: World Scientific

Published: 2011-02-25

Total Pages: 419

ISBN-13: 1908978767

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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

Computability, Complexity, and Languages
Computability, Complexity, and Languages

Author: Martin Davis

Publisher: Elsevier

Published: 1994-03-18

Total Pages: 631

ISBN-13: 0080502466

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Computability, Complexity, and Languages is an introductory text that covers the key areas of computer science, including recursive function theory, formal languages, and automata. It assumes a minimal background in formal mathematics. The book is divided into five parts: Computability, Grammars and Automata, Logic, Complexity, and Unsolvability. Computability theory is introduced in a manner that makes maximum use of previous programming experience, including a "universal" program that takes up less than a page. The number of exercises included has more than tripled. Automata theory, computational logic, and complexity theory are presented in a flexible manner, and can be covered in a variety of different arrangements.

Digital And The Real World, The: Computational Foundations Of Mathematics, Science, Technology, And Philosophy
Digital And The Real World, The: Computational Foundations Of Mathematics, Science, Technology, And Philosophy

Author: Klaus Mainzer

Publisher: World Scientific

Published: 2017-11-17

Total Pages: 471

ISBN-13: 9813225505

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In the 21st century, digitalization is a global challenge of mankind. Even for the public, it is obvious that our world is increasingly dominated by powerful algorithms and big data. But, how computable is our world? Some people believe that successful problem solving in science, technology, and economies only depends on fast algorithms and data mining. Chances and risks are often not understood, because the foundations of algorithms and information systems are not studied rigorously. Actually, they are deeply rooted in logics, mathematics, computer science and philosophy.Therefore, this book studies the foundations of mathematics, computer science, and philosophy, in order to guarantee security and reliability of the knowledge by constructive proofs, proof mining and program extraction. We start with the basics of computability theory, proof theory, and information theory. In a second step, we introduce new concepts of information and computing systems, in order to overcome the gap between the digital world of logical programming and the analog world of real computing in mathematics and science. The book also considers consequences for digital and analog physics, computational neuroscience, financial mathematics, and the Internet of Things (IoT).

Models of Computation in Context
Models of Computation in Context

Author: Benedikt Löwe

Publisher: Springer Science & Business Media

Published: 2011-06-22

Total Pages: 330

ISBN-13: 3642218741

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This book constitutes the refereed proceedings of the 7th Conference on Computability in Europe, CiE 2011, held in Sofia, Bulgaria, in June/July 2011. The 22 revised papers presented together with 11 invited lectures were carefully reviewed and selected with an acceptance rate of under 40%. The papers cover the topics computability in analysis, algebra, and geometry; classical computability theory; natural computing; relations between the physical world and formal models of computability; theory of transfinite computations; and computational linguistics.

Computation and Logic in the Real World
Computation and Logic in the Real World

Author: Barry S. Cooper

Publisher: Springer

Published: 2007-07-25

Total Pages: 843

ISBN-13: 354073001X

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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.

New Computational Paradigms
New Computational Paradigms

Author: S.B. Cooper

Publisher: Springer Science & Business Media

Published: 2007-11-28

Total Pages: 560

ISBN-13: 0387685464

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This superb exposition of a complex subject examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. This book is suitable for researchers and graduate students in mathematics, philosophy, and computer science with a special interest in logic and foundational issues. Most useful to graduate students are the survey papers on computable analysis and biological computing. Logicians and theoretical physicists will also benefit from this book.

The Foundations of Computability Theory
The Foundations of Computability Theory

Author: Borut Robič

Publisher: Springer

Published: 2015-09-14

Total Pages: 341

ISBN-13: 3662448084

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This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism; in Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability; in Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science.

Computability Theory and Applications
Computability Theory and Applications

Author: Robert I. Soare

Publisher: Springer

Published: 2016-05-09

Total Pages: 0

ISBN-13: 9783642319327

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This book emphasizes three very important concepts: computability, as opposed to recursion or induction; classical computability, i.e., algorithmic functions on certain countable structures in the original sense of Turing and Post; and the art of computability, i.e., a skill to be practiced, but also important an esthetic sense of beauty and taste in mathematics.

Computability and Logic
Computability and Logic

Author: George S. Boolos

Publisher: Cambridge University Press

Published: 2002-03-04

Total Pages: 374

ISBN-13: 9780521007580

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This fourth edition of one of the classic logic textbooks has been thoroughly revised by John Burgess. The aim is to increase the pedagogical value of the book for the core market of students of philosophy and for students of mathematics and computer science as well. This book has become a classic because of its accessibility to students without a mathematical background, and because it covers not simply the staple topics of an intermediate logic course such as Godel's Incompleteness Theorems, but also a large number of optional topics from Turing's theory of computability to Ramsey's theorem. John Burgess has now enhanced the book by adding a selection of problems at the end of each chapter, and by reorganising and rewriting chapters to make them more independent of each other and thus to increase the range of options available to instructors as to what to cover and what to defer.