Computability In Context

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Models Of Computation In Context

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Author : Benedikt Löwe
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-22

Models Of Computation In Context written by Benedikt Löwe 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 2011-06-22 with Computers categories.

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.

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 Foundations Of Computability Theory

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Author : Borut Robič
language : en
Publisher: Springer
Release Date : 2015-09-14

The Foundations Of Computability Theory written by Borut Robič and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-14 with Computers categories.

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

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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.

Higher Order Computability

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Author : John Longley
language : en
Publisher: Springer
Release Date : 2015-11-06

Higher Order Computability written by John Longley and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-06 with Computers categories.

This book offers a self-contained exposition of the theory of computability in a higher-order context, where 'computable operations' may themselves be passed as arguments to other computable operations. The subject originated in the 1950s with the work of Kleene, Kreisel and others, and has since expanded in many different directions under the influence of workers from both mathematical logic and computer science. The ideas of higher-order computability have proved valuable both for elucidating the constructive content of logical systems, and for investigating the expressive power of various higher-order programming languages. In contrast to the well-known situation for first-order functions, it turns out that at higher types there are several different notions of computability competing for our attention, and each of these has given rise to its own strand of research. In this book, the authors offer an integrated treatment that draws together many of these strands within a unifying framework, revealing not only the range of possible computability concepts but the relationships between them. The book will serve as an ideal introduction to the field for beginning graduate students, as well as a reference for advanced researchers

Automata And Computability

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Author : Anuradha A. Puntambekar
language : en
Publisher: Technical Publications
Release Date : 2020-12-01

Automata And Computability written by Anuradha A. Puntambekar and has been published by Technical Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-01 with Computers categories.

The book has been developed to provide comprehensive and consistent coverage of concepts of automata theory, formal languages and computation. This book begins by giving prerequisites for the subject, like strings, languages, types of automata, deterministic and non-deterministic automata. It proceeds forward to discuss advanced concepts like regular expressions, context free grammar and pushdown automata. The text then goes on to give a detailed description of context free and non context free languages and Turing Machine with its complexity. This compact and well-organized book provides a clear understanding of the subject with its emphasis on concepts along with a large number of examples.

Connecting With Computability

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Author : Liesbeth De Mol
language : en
Publisher: Springer Nature
Release Date : 2021-07-01

Connecting With Computability written by Liesbeth De Mol and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-01 with Computers categories.

This book constitutes the proceedings of the 17th Conference on Computability in Europe, CiE 2021, organized by the University of Ghent in July 2021. Due to COVID-19 pandemic the conference was held virtually. The 48 full papers presented in this volume were carefully reviewed and selected from 50 submissions. CiE promotes the development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences, such as physics and biology, as well as related fields, such as philosophy and history of computing. CiE 2021 had as its motto Connecting with Computability, a clear acknowledgement of the connecting and interdisciplinary nature of the conference series which is all the more important in a time where people are more than ever disconnected from one another due to the COVID-19 pandemic.

Automata And Computability

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Author : Dexter C. Kozen
language : en
Publisher: Springer
Release Date : 2013-11-11

Automata And Computability written by Dexter C. Kozen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Computers categories.

These are my lecture notes from CS381/481: Automata and Computability Theory, a one-semester senior-level course I have taught at Cornell Uni versity for many years. I took this course myself in thc fall of 1974 as a first-year Ph.D. student at Cornell from Juris Hartmanis and have been in love with the subject ever sin,:e. The course is required for computer science majors at Cornell. It exists in two forms: CS481, an honors version; and CS381, a somewhat gentler paced version. The syllabus is roughly the same, but CS481 go es deeper into thc subject, covers more material, and is taught at a more abstract level. Students are encouraged to start off in one or the other, then switch within the first few weeks if they find the other version more suitaLle to their level of mathematical skill. The purpose of t.hc course is twofold: to introduce computer science students to the rieh heritage of models and abstractions that have arisen over the years; and to dew!c'p the capacity to form abstractions of their own and reason in terms of them.

Automata And Computability Insights

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Author : Anasooya Khanna
language : en
Publisher: Educohack Press
Release Date : 2025-02-20

Automata And Computability Insights written by Anasooya Khanna and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Computers categories.

"Automata and Computability Insights" is a foundational textbook that delves into the theoretical underpinnings of computer science, exploring automata theory, formal languages, and computability. Authored by Dexter C. Kozen, this book provides a deep understanding of these concepts for students, researchers, and educators. Beginning with a thorough introduction to formal languages and automata, the book covers finite automata, regular languages, context-free languages, and context-free grammars. It offers insightful discussions on pushdown automata and their expressive power. The book also explores decidability and undecidability, including the Halting Problem and decision procedures, providing a profound understanding of computational systems' limitations and capabilities. Advanced topics such as quantum computing, oracle machines, and hypercomputation push the boundaries of traditional computational models. The book bridges theory and real-world applications with chapters on complexity theory, NP-completeness, and parallel and distributed computing. This interdisciplinary approach integrates mathematical rigor with computer science concepts, making it suitable for undergraduate and graduate courses. "Automata and Computability Insights" is a valuable reference for researchers, presenting complex topics clearly and facilitating engagement with numerous exercises and examples. It equips readers with the tools to analyze and understand the efficiency of algorithms and explore open problems in theoretical computation.

Theories Of Computability

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Author : Nicholas Pippenger
language : en
Publisher: Cambridge University Press
Release Date : 1997-05-28

Theories Of Computability written by Nicholas Pippenger 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 1997-05-28 with Computers categories.

A mathematically sophisticated introduction to Turing's theory, Boolean functions, automata, and formal languages.