Computation Proof Machine
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Author | : Gilles Dowek |
Publisher | : Cambridge University Press |
Total Pages | : 161 |
Release | : 2015-05-05 |
Genre | : 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 | : Sanjeev Arora |
Publisher | : Cambridge University Press |
Total Pages | : 609 |
Release | : 2009-04-20 |
Genre | : Computers |
ISBN | : 0521424267 |
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Author | : Peter J. Denning |
Publisher | : Prentice Hall |
Total Pages | : 632 |
Release | : 1978 |
Genre | : Computers |
ISBN | : |
Author | : Song Y. Yan |
Publisher | : World Scientific |
Total Pages | : 424 |
Release | : 1998 |
Genre | : 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 | : M. Kara |
Publisher | : IOS Press |
Total Pages | : 236 |
Release | : 1996 |
Genre | : 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 | : Jérôme Durand-Lose |
Publisher | : Springer |
Total Pages | : 187 |
Release | : 2018-06-04 |
Genre | : Computers |
ISBN | : 3319924028 |
This book constitutes the refereed proceedings of the 8th International Conference on Machines, Computations, and Universality, MCU 2018, held in Fontainebleau, France, in June 2018. The 9 revised full papers presented together with 5 invited talks were carefully reviewed and selected from numerous submissions. MCU explores computation in the setting of various discrete models (Turing machines, register machines, cellular automata, tile assembly systems, rewriting systems, molecular computing models, neural models, concurrent systems, etc.) and analog and hybrid models (BSS machines, infinite time cellular automata, real machines, quantum computing, etc.).
Author | : Martin Davis |
Publisher | : |
Total Pages | : 40 |
Release | : 1961 |
Genre | : Calculus of variations |
ISBN | : |
The programming of a proof procedure is discussed in connection with trial runs and possible improvements. (Author).
Author | : Lawrence C. Paulson |
Publisher | : |
Total Pages | : 302 |
Release | : 1987 |
Genre | : 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 | : Gilles Dowek |
Publisher | : Springer Science & Business Media |
Total Pages | : 161 |
Release | : 2011-01-11 |
Genre | : 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 | : John MacCormick |
Publisher | : Princeton University Press |
Total Pages | : 404 |
Release | : 2018-05-01 |
Genre | : 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