Computation And Its Limits
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Computation and Its Limits
Author: Paul Cockshott
language: en
Publisher: Oxford University Press
Release Date: 2012-03-15
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.
Hypercomputation
Author: Apostolos Syropoulos
language: en
Publisher: Springer Science & Business Media
Release Date: 2008-12-10
Hypercomputation is a relatively new theory of computation that is about computing methods and devices that transcend the so-called Church-Turing thesis. This book will provide a thorough description of the field of hypercomputation covering all attempts at devising conceptual hypermachines and all new promising computational paradigms that may eventually lead to the construction of a hypermachine. Readers of this book will get a deeper understanding of what computability is and why the Church-Turing thesis poses an arbitrary limit to what can be actually computed. Hypercomputing is in and of itself quite a novel idea and as such the book will be interesting in its own right. The most important features of the book, however, will be the thorough description of the various attempts of hypercomputation: from trial-and-error machines to the exploration of the human mind, if we treat it as a computing device.
Mathematics and Computation
Author: Avi Wigderson
language: en
Publisher: Princeton University Press
Release Date: 2019-10-29
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography