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Evolving Computability
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Book Synopsis Evolving Computability by : Arnold Beckmann
Download or read book Evolving Computability written by Arnold Beckmann and published by Springer. This book was released on 2015-06-19 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 11th Conference on Computability in Europe, CiE 2015, held in Bucharest, Romania, in June/July 2015. The 26 revised papers presented were carefully reviewed and selected from 64 submissions and included together with 10 invited papers in this proceedings. The conference CiE 2015 has six special sessions: two sessions, Representing Streams and Reverse Mathematics, were introduced for the first time in the conference series. In addition to this, new developments in areas frequently covered in the CiE conference series were addressed in the further special sessions on Automata, Logic and Infinite Games; Bio-inspired Computation; Classical Computability Theory; as well as History and Philosophy of Computing.
Book Synopsis The Foundations of Computability Theory by : Borut Robič
Download or read book The Foundations of Computability Theory written by Borut Robič and published by Springer Nature. This book was released on 2020-11-13 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Finally, in the new Part IV the author revisits the computability (Church-Turing) thesis in greater detail. He offers a systematic and detailed account of its origins, evolution, and meaning, he describes more powerful, modern versions of the thesis, and he discusses recent speculative proposals for new computing paradigms such as hypercomputing. 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. This new edition is completely revised, with almost one hundred pages of new material. In particular the author applied more up-to-date, more consistent terminology, and he addressed some notational redundancies and minor errors. He developed a glossary relating to computability theory, expanded the bibliographic references with new entries, and added the new part described above and other new sections.
Book Synopsis Logic and Theory of Algorithms by : Arnold Beckmann
Download or read book Logic and Theory of Algorithms written by Arnold Beckmann and published by Springer Science & Business Media. This book was released on 2008-06-03 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 4th International Conference on Computability in Europe, CiE 2008, held in Athens, Greece, in June 2008. The 36 revised full papers presented together with 25 invited tutorials and lectures were carefully reviewed and selected from 108 submissions. Among them are papers of 6 special sessions entitled algorithms in the history of mathematics, formalising mathematics and extracting algorithms from proofs, higher-type recursion and applications, algorithmic game theory, quantum algorithms and complexity, and biology and computation.
Book Synopsis Ordinal Computability by : Merlin Carl
Download or read book Ordinal Computability written by Merlin Carl and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-09-23 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs on all areas of mathematical logic and its applications. It is addressed to advanced students and research mathematicians, and may also serve as a guide for lectures and for seminars at the graduate level.
Book Synopsis Beyond the Horizon of Computability by : Marcella Anselmo
Download or read book Beyond the Horizon of Computability written by Marcella Anselmo and published by Springer Nature. This book was released on 2020-06-23 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 16th Conference on Computability in Europe, CiE 2020, which was planned to be held in Fisciano, Italy, during June 29 until July 3, 2020. The conference moved to a virtual format due to the coronavirus pandemic. The 30 full and 5 short papers presented in this volume were carefully reviewed and selected from 72 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 2020 had as its motto Beyond the Horizon of Computability, reflecting the interest of CiE in research transgressing the traditional boundaries of computability theory.
Book Synopsis Theory and Practice of Natural Computing by : Carlos Martín-Vide
Download or read book Theory and Practice of Natural Computing written by Carlos Martín-Vide and published by Springer Nature. This book was released on 2019-11-22 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 8th International Conference on Theory and Practice of Natural Computing, TPNC 2019, held in Kingston, ON, Canada, in December 2019. The 15 full papers presented in this book, together with two invited talk, were carefully reviewed and selected from 38 submissions. The papers are organized in topical sections named: Applications of Natural Computing; Evolutionary Computation; Genetic Algorithms, Swarm Intelligence, and Heuristics; Quantum Computing and Information.
Book Synopsis Handbook of Computability and Complexity in Analysis by : Vasco Brattka
Download or read book Handbook of Computability and Complexity in Analysis written by Vasco Brattka and published by Springer Nature. This book was released on 2021-06-04 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computable analysis is the modern theory of computability and complexity in analysis that arose out of Turing's seminal work in the 1930s. This was motivated by questions such as: which real numbers and real number functions are computable, and which mathematical tasks in analysis can be solved by algorithmic means? Nowadays this theory has many different facets that embrace topics from computability theory, algorithmic randomness, computational complexity, dynamical systems, fractals, and analog computers, up to logic, descriptive set theory, constructivism, and reverse mathematics. In recent decades computable analysis has invaded many branches of analysis, and researchers have studied computability and complexity questions arising from real and complex analysis, functional analysis, and the theory of differential equations, up to (geometric) measure theory and topology. This handbook represents the first coherent cross-section through most active research topics on the more theoretical side of the field. It contains 11 chapters grouped into parts on computability in analysis; complexity, dynamics, and randomness; and constructivity, logic, and descriptive complexity. All chapters are written by leading experts working at the cutting edge of the respective topic. Researchers and graduate students in the areas of theoretical computer science and mathematical logic will find systematic introductions into many branches of computable analysis, and a wealth of information and references that will help them to navigate the modern research literature in this field.
Book Synopsis Mathematics and Computation by : Avi Wigderson
Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Book Synopsis Unconventional Computation and Natural Computation by : Martyn Amos
Download or read book Unconventional Computation and Natural Computation written by Martyn Amos and published by Springer. This book was released on 2016-06-17 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 15th International Conference on Unconventional Computation and Natural Computation, UCNC 2016, held in Manchester, UK, in July 2016. The 15 revised full papers presented together with 5 invited papers were carefully reviewed and selected from 30 submissions. The papers cover a wide range of topics including molecular, cellular, quantum, optical and chaos computing; cellular automata; neural and evolutionary computation; artificial immune systems; Ant algorithms and swarm intelligence; amorphous computing; membrane computing; computational systems biology and computational neuroscience; and synthetic biology.
Book Synopsis A Computable Universe by : Hector Zenil
Download or read book A Computable Universe written by Hector Zenil and published by World Scientific. This book was released on 2013 with total page 855 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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?
Book Synopsis Computable Foundations for Economics by : K. Vela Velupillai
Download or read book Computable Foundations for Economics written by K. Vela Velupillai and published by Routledge. This book was released on 2012-07-26 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computable Foundations for Economics is a unified collection of essays, some of which are published here for the first time and all of which have been updated for this book, on an approach to economic theory from the point of view of algorithmic mathematics. By algorithmic mathematics the author means computability theory and constructive mathematics. This is in contrast to orthodox mathematical economics and game theory, which are formalised with the mathematics of real analysis, underpinned by what is called the ZFC formalism, i.e., set theory with the axiom of choice. This reliance on ordinary real analysis and the ZFC system makes economic theory in its current mathematical mode completely non-algorithmic, which means it is numerically meaningless. The book provides a systematic attempt to dissect and expose the non-algorithmic content of orthodox mathematical economics and game theory and suggests a reformalization on the basis of a strictly rigorous algorithmic mathematics. This removes the current schizophrenia in mathematical economics and game theory, where theory is entirely divorced from algorithmic applicability – for experimental and computational exercises. The chapters demonstrate the uncomputability and non-constructivity of core areas of general equilibrium theory, game theory and recursive macroeconomics. The book also provides a fresh look at the kind of behavioural economics that lies behind Herbert Simon’s work, and resurrects a role for the noble classical traditions of induction and verification, viewed and formalised, now, algorithmically. It will therefore be of particular interest to postgraduate students and researchers in algorithmic economics, game theory and classical behavioural economics.
Book Synopsis Computable, Constructive & Behavioural Economic Dynamics by : Stefano Zambelli
Download or read book Computable, Constructive & Behavioural Economic Dynamics written by Stefano Zambelli and published by Routledge. This book was released on 2010-02-25 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains thirty original articles dealing with important aspects of theoretical as well as applied economic theory. While the principal focus is on: the computational and algorithmic nature of economic dynamics; individual as well as collective decision process and rational behavior, some contributions emphasize also the importance of classical recursion theory and constructive mathematics for dynamical systems, business cycles theories, growth theories, and others are in the area of history of thought, methodology and behavioural economics. The contributors range from Nobel Laureates to the promising new generation of innovative thinkers. This volume is also a Festschrift in honour of Professor Kumaraswamy Vela Velupillai, the founder of Computable Economics, a growing field of research where important results stemming from classical recursion theory and constructive mathematics are applied to economic theory. The aim and hope is to provide new tools for economic modelling. This book will be of particular appeal to postgraduate students and scholars in one or more of the following fields: computable economics, business cycles, macroeconomics, growth theories, methodology, behavioural economics, financial economics, experimental and agent based economics. It might be also of importance to those interested on the general theme of algorithmic foundations for social sciences.
Book Synopsis The Evolution of Time: Studies of Time in Science, Anthropology, Theology by : Argyris Nicolaidis
Download or read book The Evolution of Time: Studies of Time in Science, Anthropology, Theology written by Argyris Nicolaidis and published by Bentham Science Publishers. This book was released on 2013-05-27 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time - a fundamental component of human thought and experience - is quite enigmatic and elusive when it comes to defining it. In The Evolution of Time: Studies of Time in Science, Anthropology, Theology scholars from the fields of physics, mathematics, biology, neuroscience, psychology, philosophy and theology draw from their own field of knowledge and expertise and present their understanding of the time phenomenon. Time as a dynamic interplay of being and becoming, the different temporalities we encounter in nature, the human dimension of time, are all important issues presented and thoroughly analyzed in the e-book. The e-book has a manifest trans-disciplinary character and it is a suitable for readers interested in evolution, the dynamics of time and the complexity of our own conceptions of time.
Book Synopsis Randomness & Undecidability in Physics by : Karl Svozil
Download or read book Randomness & Undecidability in Physics written by Karl Svozil and published by World Scientific. This book was released on 1993 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent findings in the computer sciences, discrete mathematics, formal logics and metamathematics have opened up a royal road for the investigation of undecidability and randomness in physics. A translation of these formal concepts yields a fresh look into diverse features of physical modelling such as quantum complementarity and the measurement problem, but also stipulates questions related to the necessity of the assumption of continua.Conversely, any computer may be perceived as a physical system: not only in the immediate sense of the physical properties of its hardware. Computers are a medium to virtual realities. The foreseeable importance of such virtual realities stimulates the investigation of an ?inner description?, a ?virtual physics? of these universes of computation. Indeed, one may consider our own universe as just one particular realisation of an enormous number of virtual realities, most of them awaiting discovery.One motive of this book is the recognition that what is often referred to as ?randomness? in physics might actually be a signature of undecidability for systems whose evolution is computable on a step-by-step basis. To give a flavour of the type of questions envisaged: Consider an arbitrary algorithmic system which is computable on a step-by-step basis. Then it is in general impossible to specify a second algorithmic procedure, including itself, which, by experimental input-output analysis, is capable of finding the deterministic law of the first system. But even if such a law is specified beforehand, it is in general impossible to predict the system behaviour in the ?distant future?. In other words: no ?speedup? or ?computational shortcut? is available. In this approach, classical paradoxes can be formally translated into no-go theorems concerning intrinsic physical perception.It is suggested that complementarity can be modelled by experiments on finite automata, where measurements of one observable of the automaton destroys the possibility to measure another observable of the same automaton and it vice versa.Besides undecidability, a great part of the book is dedicated to a formal definition of randomness and entropy measures based on algorithmic information theory.
Book Synopsis Computable, Constructive and Behavioural Economic Dynamics by : Stefano Zambelli
Download or read book Computable, Constructive and Behavioural Economic Dynamics written by Stefano Zambelli and published by Routledge. This book was released on 2010-02-25 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains thirty original articles dealing with important aspects of theoretical as well as applied economic theory. While the principal focus is on: the computational and algorithmic nature of economic dynamics; individual as well as collective decision process and rational behavior, some contributions emphasize also the importance of classical recursion theory and constructive mathematics for dynamical systems, business cycles theories, growth theories, and others are in the area of history of thought, methodology and behavioural economics. The contributors range from Nobel Laureates to the promising new generation of innovative thinkers. This volume is also a Festschrift in honour of Professor Kumaraswamy Vela Velupillai, the founder of Computable Economics, a growing field of research where important results stemming from classical recursion theory and constructive mathematics are applied to economic theory. The aim and hope is to provide new tools for economic modelling. This book will be of particular appeal to postgraduate students and scholars in one or more of the following fields: computable economics, business cycles, macroeconomics, growth theories, methodology, behavioural economics, financial economics, experimental and agent based economics. It might be also of importance to those interested on the general theme of algorithmic foundations for social sciences.
Book Synopsis Language Evolution by : Rudolf Botha
Download or read book Language Evolution written by Rudolf Botha and published by Cambridge University Press. This book was released on 2016-03-02 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: How can we unravel the evolution of language, given that there is no direct evidence about it? Rudolf Botha addresses this intriguing question in his fascinating new book. Inferences can be drawn about language evolution from a range of other phenomena, serving as windows into this prehistoric process. These include shell-beads, fossil skulls and ancestral brains, modern pidgin and creole languages, homesign systems and emergent sign languages, modern motherese, language use of modern hunter-gatherers, first language acquisition, similarities between language and music, and comparative animal behaviour. The first systematic analysis of the Windows Approach, it will be of interest to students and researchers in many disciplines, including anthropology, archaeology, linguistics, palaeontology and primatology, as well as anyone interested in how language evolved.
Book Synopsis Proof And Computation: Digitization In Mathematics, Computer Science And Philosophy by : Klaus Mainzer
Download or read book Proof And Computation: Digitization In Mathematics, Computer Science And Philosophy written by Klaus Mainzer and published by World Scientific. This book was released on 2018-05-30 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisciplinary point of view. Its scope includes Predicative Foundations, Constructive Mathematics and Type Theory, Computation in Higher Types, Extraction of Programs from Proofs, and Algorithmic Aspects in Financial Mathematics. By filling the gap between (under-)graduate level textbooks and advanced research papers, the book gives a scholarly account of recent developments and emerging branches of the aforementioned fields.
