Author : Gilles Dowek
Publisher : Cambridge University Press
Page : 161 pages
File Size : 18,87 MB
Release : 2015-05-05
Category : Computers
ISBN : 0521118018
Computation, calculation, algorithms - all have played an important role in mathematical progress from the beginning - but behind the scenes, their contribution was obscured in the enduring mathematical literature. To understand the future of mathematics, this fascinating book returns to its past, tracing the hidden history that follows the thread of computation.
Author : Song Y. Yan
Publisher : World Scientific
Page : 424 pages
File Size : 16,36 MB
Release : 1998
Category : Computers
ISBN : 9789810234225
This book provides a concise and modern introduction to Formal Languages and Machine Computation, a group of disparate topics in the theory of computation, which includes formal languages, automata theory, turing machines, computability, complexity, number-theoretic computation, public-key cryptography, and some new models of computation, such as quantum and biological computation. As the theory of computation is a subject based on mathematics, a thorough introduction to a number of relevant mathematical topics, including mathematical logic, set theory, graph theory, modern abstract algebra, and particularly number theory, is given in the first chapter of the book. The book can be used either as a textbook for an undergraduate course, for a first-year graduate course, or as a basic reference in the field.
Author : Lawrence C. Paulson
Publisher :
Page : 302 pages
File Size : 19,39 MB
Release : 1987
Category : Computers
ISBN : 9780521346320
This book is concerned with techniques for formal theorem-proving, with particular reference to Cambridge LCF (Logic for Computable Functions). Cambridge LCF is a computer program for reasoning about computation. It combines the methods of mathematical logic with domain theory, the basis of the denotational approach to specifying the meaning of program statements. Cambridge LCF is based on an earlier theorem-proving system, Edinburgh LCF, which introduced a design that gives the user flexibility to use and extend the system. A goal of this book is to explain the design, which has been adopted in several other systems. The book consists of two parts. Part I outlines the mathematical preliminaries, elementary logic and domain theory, and explains them at an intuitive level, giving reference to more advanced reading; Part II provides sufficient detail to serve as a reference manual for Cambridge LCF. It will also be a useful guide for implementors of other programs based on the LCF approach.
Author : Sanjeev Arora
Publisher : Cambridge University Press
Page : 609 pages
File Size : 47,10 MB
Release : 2009-04-20
Category : Computers
ISBN : 0521424267
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Author : M. Kara
Publisher : IOS Press
Page : 236 pages
File Size : 26,96 MB
Release : 1996
Category : Computers
ISBN : 9789051992670
Abstract Machine Models have played a profound though frequently unacknowledged role in the development of modern computing systems. They provide a precise definition of vital concepts, allow system complexity to be managed by providing appropriate views of the activity under consideration, enable reasoning about the correctness and quantitative performance of proposed problem solutions, and encourage communication through a common medium of expression. Abstract Models in Parallel and Distributed computing have a particularly important role in the development of contemporary systems, encapsulating and controlling an inherently high degree of complexity. The Parallel and Distributed computing communities have traditionally considered themselves to be separate. However, there is a significant contemporary interest in both of these communities in a common hardware model; a set of workstation-class machines connected by a high-performance network. The traditional Parallel/Distributed distinction therefore appears under threat.
Author : Peter J. Denning
Publisher : Prentice Hall
Page : 632 pages
File Size : 17,45 MB
Release : 1978
Category : Computers
ISBN :
Author : John MacCormick
Publisher : Princeton University Press
Page : 404 pages
File Size : 50,72 MB
Release : 2018-05-01
Category : Computers
ISBN : 0691170665
An accessible and rigorous textbook for introducing undergraduates to computer science theory What Can Be Computed? is a uniquely accessible yet rigorous introduction to the most profound ideas at the heart of computer science. Crafted specifically for undergraduates who are studying the subject for the first time, and requiring minimal prerequisites, the book focuses on the essential fundamentals of computer science theory and features a practical approach that uses real computer programs (Python and Java) and encourages active experimentation. It is also ideal for self-study and reference. The book covers the standard topics in the theory of computation, including Turing machines and finite automata, universal computation, nondeterminism, Turing and Karp reductions, undecidability, time-complexity classes such as P and NP, and NP-completeness, including the Cook-Levin Theorem. But the book also provides a broader view of computer science and its historical development, with discussions of Turing's original 1936 computing machines, the connections between undecidability and Gödel's incompleteness theorem, and Karp's famous set of twenty-one NP-complete problems. Throughout, the book recasts traditional computer science concepts by considering how computer programs are used to solve real problems. Standard theorems are stated and proven with full mathematical rigor, but motivation and understanding are enhanced by considering concrete implementations. The book's examples and other content allow readers to view demonstrations of—and to experiment with—a wide selection of the topics it covers. The result is an ideal text for an introduction to the theory of computation. An accessible and rigorous introduction to the essential fundamentals of computer science theory, written specifically for undergraduates taking introduction to the theory of computation Features a practical, interactive approach using real computer programs (Python in the text, with forthcoming Java alternatives online) to enhance motivation and understanding Gives equal emphasis to computability and complexity Includes special topics that demonstrate the profound nature of key ideas in the theory of computation Lecture slides and Python programs are available at whatcanbecomputed.com
Author : Gilles Dowek
Publisher : Springer Science & Business Media
Page : 161 pages
File Size : 29,45 MB
Release : 2011-01-11
Category : Computers
ISBN : 0857291211
Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation. Proofs and Algorithms: Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a proof, a computable function, a model and a set. It presents a series of results, both positive and negative, - Church's undecidability theorem, Gödel’s incompleteness theorem, the theorem asserting the semi-decidability of provability - that have profoundly changed our vision of reasoning, computation, and finally truth itself. Designed for undergraduate students, this book presents all that philosophers, mathematicians and computer scientists should know about logic.
Author : Martin Davis
Publisher :
Page : 40 pages
File Size : 27,36 MB
Release : 1961
Category : Calculus of variations
ISBN :
The programming of a proof procedure is discussed in connection with trial runs and possible improvements. (Author).
Author : Maurice Margenstern
Publisher : Springer
Page : 329 pages
File Size : 28,54 MB
Release : 2003-06-29
Category : Computers
ISBN : 3540451323
In the ?rst part of the present volume of LNCS, the reader will ?nd the invited talks given at the MCU 2001 conference. In the second part, he/she will ?nd the contributions that were presented at the conference after selection. In both cases, papers are arranged in the alphabetical order of the authors. MCU 2001 is the third conference in theoretical computer science, Machines, computations and universality, formerly, Machines et calculs universels. Both previous conferences, MCU’95 and MCU’98, were organized by Maurice M- genstern in Paris and in Metz (France), respectively. From the very beginning, MCU conferences have been an international sci- ti?c event. For the third conference, in order to stress that aspect, it was decided to hold it outside France. Moldova was chosen thanks to the close cooperation between the present chairmen of MCU 2001. MCU 2001 also aims at high scienti?c standards. We hope that the present volume will convince the reader that the tradition of previous conferences have been upheld by this one. Cellular automata and molecular computing are well represented in this volume. And this is also the case for quantum computing, f- mal languages, and the theory of automata. MCU 2001 does not fail its tradition of providing our community with important results on Turing machines.
