[PDF] Combinatorics Computability And Logic eBook

Author : C.S. Calude
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 38,75 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1447107179

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This volume contains the papers presented at the Third Discrete Mathematics and Theoretical Computer Science Conference (DMTCS1), which was held at 'Ovidius'University Constantza, Romania in July 2001. The conference was open to all areas of discrete mathematics and theoretical computer science, and the papers contained within this volume cover topics such as: abstract data types and specifications; algorithms and data structures; automata and formal languages; computability, complexity and constructive mathematics; discrete mathematics, combinatorial computing and category theory; logic, nonmonotonic logic and hybrid systems; molecular computing.

Author : Martin Davis
Publisher : Courier Corporation
Page : 292 pages
File Size : 49,51 MB
Release : 2013-04-16
Category : Mathematics
ISBN : 0486151069

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Classic graduate-level introduction to theory of computability. Discusses general theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general theory, mathematical logic, Kleene hierarchy, more.

Author : George Boolos
Publisher : Harvard University Press
Page : 458 pages
File Size : 19,3 MB
Release : 1998
Category : Mathematics
ISBN : 9780674537675

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George Boolos was one of the most prominent and influential logician-philosophers of recent times. This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; on Frege, Dedekind, Cantor, and Russell; and on miscellaneous topics in logic and proof theory, including three papers on various aspects of the Gödel theorems. Boolos is universally recognized as the leader in the renewed interest in studies of Frege's work on logic and the philosophy of mathematics. John Burgess has provided introductions to each of the three parts of the volume, and also an afterword on Boolos's technical work in provability logic, which is beyond the scope of this volume.

Author : Douglas S. Bridges
Publisher :
Page : 440 pages
File Size : 25,18 MB
Release : 1997
Category : Computers
ISBN :

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DMTCS'96 is the first of a planned series of conferences organized by the Centre for Discrete Mathematics and Theoretical Computer Science, and is the first joint venture of the Computer Science and Mathematics departments of the University of Auckland and Waikato, New Zealand. These proceedings contain original papers which had been solicited in all areas of discrete mathematics and theoretical computer science, in particular in the areas of combinatorics, complexity, computability, constructivity, and logic.

Author : Denis R Hirschfeldt
Publisher : World Scientific
Page : 231 pages
File Size : 48,46 MB
Release : 2014-07-18
Category : Mathematics
ISBN : 9814612634

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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.

Author : Peter M. Schuster
Publisher : Springer Nature
Page : 391 pages
File Size : 15,79 MB
Release : 2020-01-01
Category : Philosophy
ISBN : 3030302296

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This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven to be extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students.

Author : Douglas Cenzer
Publisher : World Scientific
Page : 387 pages
File Size : 42,38 MB
Release : 2020-10-02
Category : Mathematics
ISBN : 9813228245

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This volume presents some exciting new developments occurring on the interface between set theory and computability as well as their applications in algebra, analysis and topology. These include effective versions of Borel equivalence, Borel reducibility and Borel determinacy. It also covers algorithmic randomness and dimension, Ramsey sets and Ramsey spaces. Many of these topics are being discussed in the NSF-supported annual Southeastern Logic Symposium.

Author : J. Roger Hindley
Publisher : Cambridge University Press
Page : 358 pages
File Size : 44,10 MB
Release : 2008-07-24
Category : Computers
ISBN : 9780521898850

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Combinatory logic and lambda-calculus, originally devised in the 1920's, have since developed into linguistic tools, especially useful in programming languages. The authors' previous book served as the main reference for introductory courses on lambda-calculus for over 20 years: this long-awaited new version is thoroughly revised and offers a fully up-to-date account of the subject, with the same authoritative exposition. The grammar and basic properties of both combinatory logic and lambda-calculus are discussed, followed by an introduction to type-theory. Typed and untyped versions of the systems, and their differences, are covered. Lambda-calculus models, which lie behind much of the semantics of programming languages, are also explained in depth. The treatment is as non-technical as possible, with the main ideas emphasized and illustrated by examples. Many exercises are included, from routine to advanced, with solutions to most at the end of the book.

Author : C.S. Calude
Publisher : Springer
Page : 0 pages
File Size : 41,13 MB
Release : 1999-04-01
Category : Mathematics
ISBN : 9789814021562

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This volume contains the proceedings of the 2nd International Conference on Discrete Mathematics and Theoretical Computer Science (DMTCS9) and the 5th Australasian Theory Symposium (CATS9). Both were held as part of the Australasian Computer Science Week (ACSW9) in Auckland, New Zealand, January 1999. The topics presented included those on: abstract data types and specifications; algorithms and data structures; automata and formal languages; computability and complexity; computational algebras, biology, geometry, logic, and number theory; concurrency, distributed systems, and parallel computing; constructive mathematics; discrete mathematics and combinatorial computing; formal semantics, specification, synthesis, and verification. These proceedings, comprised of 5 invited papers and 19 contributed refereed papers, thus provide the latest research in these fields.