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Computability And Models

Author: Barry S. Cooper
Publisher: Springer Science & Business Media
ISBN: 1461507553
Size: 45.41 MB
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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.

Unconventional Computation

Author: Christian S. Calude
Publisher: Springer Science & Business Media
ISBN: 3540851933
Size: 73.97 MB
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This book constitutes the refereed proceedings of the 7th International Conference on Unconventional Computation, UC 2008, held in Vienna, Austria, in August 2008. The 16 revised full papers presented together with 4 invited papers were carefully reviewed and selected for inclusion in the book. The papers are devoted to all aspects of unconventional computation ranging from theoretical and experimental aspects to various applications. Typical topics are: natural computing including quantum, cellular, molecular, neural and evolutionary computing, chaos and dynamical system-based computing, and various proposals for computations that go beyond the Turing model.

Sofsem 2006 Theory And Practice Of Computer Science

Author: Jirí Wiedermann
Publisher: Springer
ISBN: 3540322175
Size: 74.19 MB
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This book presents the proceedings of the 32nd Conference on Current Trends in Theory and Practice of Computer Science, held in Merin, Czech Republic. The 45 revised full papers, presented together with 10 invited contributions were carefully reviewed and selected from 157 submissions. The papers were organized in four topical tracks on computer science foundations, wireless, mobile, ad hoc and sensor networks, database technologies, and semantic Web technologies.

Mathematical Problems From Applied Logic Ii

Author: Dov Gabbay
Publisher: Springer Science & Business Media
ISBN: 0387692452
Size: 51.68 MB
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This book presents contributions from world-renowned logicians, discussing important topics of logic from the point of view of their further development in light of requirements arising from successful application in Computer Science and AI language. Coverage includes: the logic of provability, computability theory applied to biology, psychology, physics, chemistry, economics, and other basic sciences; computability theory and computable models; logic and space-time geometry; hybrid systems; logic and region-based theory of space.

Three Views Of Logic

Author: Donald W. Loveland
Publisher: Princeton University Press
ISBN: 140084875X
Size: 13.12 MB
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Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic Treats traditional logic in a modern format Presents relevance logic with applications Provides an ideal text for a variety of one-semester upper-level undergraduate courses

Slicing The Truth

Author: Denis R Hirschfeldt
Publisher: World Scientific
ISBN: 9814612634
Size: 20.80 MB
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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. Contents:Setting Off: An IntroductionGathering Our Tools: Basic Concepts and NotationFinding Our Path: König's Lemma and ComputabilityGauging Our Strength: Reverse MathematicsIn Defense of DisarrayAchieving Consensus: Ramsey's TheoremPreserving Our Power: ConservativityDrawing a Map: Five DiagramsExploring Our Surroundings: The World Below RT22Charging Ahead: Further TopicsLagniappe: A Proof of Liu's Theorem Readership: Graduates and researchers in mathematical logic. Key Features:This book assumes minimal background in mathematical logic and takes the reader all the way to current research in a highly active areaIt is the first detailed introduction to this particular approach to this area of researchThe combination of fully worked out arguments and exercises make this book well suited to self-study by graduate students and other researchers unfamiliar with the areaKeywords:Reverse Mathematics;Computability Theory;Computable Mathematics;Computable Combinatorics