Автор: Cockshott, Paul; Mackenzie, Lewis M.; Michaelson, Название: Computation and its Limits ISBN: 019872912X ISBN-13(EAN): 9780198729129 Издательство: Oxford Academ Рейтинг: Цена: 3970 р. Наличие на складе: Поставка под заказ.
Описание: Although we are entirely unaware of it, computation is central to all aspects of our existences. Every day we solve, or try to solve, a myriad of problems, from the utterly trivial to the bafflingly complex. This book explains why it is possible to do computation and what the ultimate limits of it are, as understood by modern science.
Описание: This book is the final version of a course on algorithmic information theory and the epistemology of mathematics and physics. It discusses Einstein and Goedel's views on the nature of mathematics in the light of information theory, and sustains the thesis that mathematics is quasi-empirical. There is a foreword by Cris Calude of the University of Auckland, and supplementary material is available at the author's web site. The special feature of this book is that it presents a new "hands on" didatic approach using LISP and Mathematica software. The reader will be able to derive an understanding of the close relationship between mathematics and physics. "The Limits of Mathematics is a very personal and idiosyncratic account of Greg Chaitin's entire career in developing algorithmic information theory. The combination of the edited transcripts of his three introductory lectures maintains all the energy and content of the oral presentations, while the material on AIT itself gives a full explanation of how to implement Greg's ideas on real computers for those who want to try their hand at furthering the theory." (John Casti, Santa Fe Institute)
Описание: Combinational optimization (CO) is a topic in applied mathematics, decision science and computer science that consists of finding the best solution from a non-exhaustive search. CO is related to disciplines such as computational complexity theory and algorithm theory, and has important applications in fields such as operations research/management science, artificial intelligence, machine learning, and software engineering.Advances in Combinatorial Optimization presents a generalized framework for formulating hard combinatorial optimization problems (COPs) as polynomial sized linear programs. Though developed based on the 'traveling salesman problem' (TSP), the framework allows for the formulating of many of the well-known NP-Complete COPs directly (without the need to reduce them to other COPs) as linear programs, and demonstrates the same for three other problems (e.g. the 'vertex coloring problem' (VCP)). This work also presents new proof of the equality of the complexity classes "P" (polynomial time) and "NP" (nondeterministic polynomial time), and makes a contribution to the theory and application of 'extended formulations' (EFs).On a whole, Advances in Combinatorial Optimization offers new modeling and solution perspectives which will be useful to professionals, graduate students and researchers who are either involved in routing, scheduling and sequencing decision-making in particular, or in dealing with the theory of computing in general.
Автор: Cockshott, Paul; Mackenzie, Lewis M; Michaelson, G Название: Computation and its Limits ISBN: 0199640327 ISBN-13(EAN): 9780199640324 Издательство: Oxford Academ Рейтинг: Цена: 7121 р. Наличие на складе: Поставка под заказ.
Описание: Computation and its Limits is an innovative cross-disciplinary investigation of the relationship between computing and physical reality. It begins by exploring the mystery of why mathematics is so effective in science and seeks to explain this in terms of the modelling of one part of physical reality by another. Going from the origins of counting to the most blue-skies proposals for novel methods of computation, the authors investigate the extent to which the laws of nature and of logic constrain what we can compute. In the process they examine formal computability, the thermodynamics of computation and the promise of quantum computing.
Описание: This volume, which contains chapters written by reputable researchers, provides the state of the art in theory and algorithms for the traveling salesman problem (TSP). The book covers all important areas of study on TSP, including polyhedral theory for symmetric and asymmetric TSP, branch and bound, and branch and cut algorithms, probabilistic aspects of TSP, thorough computational analysis of heuristic and metaheuristic algorithms, theoretical analysis of approximation algorithms, including the emerging area of domination analysis of algorithms, discussion of TSP software and variations of TSP such as bottleneck TSP, generalized TSP, prize collecting TSP, maximizing TSP, orienteering problem, etc. The book is appropriate as a reference work or as a main or supplemental textbook in graduate and senior undergraduate courses and projects.
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