Mathematical Theory Of Computation
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Mathematical Theory of Computation
With the objective of making into a science the art of verifying computer programs (debugging), the author addresses both practical and theoretical aspects of the process. A classic of sequential program verification, this volume has been translated into almost a dozen other languages and is much in demand among graduate and advanced undergraduate computer science students. Subjects include computability (with discussions of finite automata and Turing machines); predicate calculus (basic notions, natural deduction, and the resolution method); verification of programs (both flowchart and algol-like programs); flowchart schemas (basic notions, decision problems, formalization in predicate calculus, and translation programs); and the fixpoint theory of programs (functions and functionals, recursive programs, and verification programs). The treamtent is self-contained, and each chapter concludes with bibliographic remarks, references, and problems.
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
Artificial and Mathematical Theory of Computation
Artificial and Mathematical Theory of Computation is a collection of papers that discusses the technical, historical, and philosophical problems related to artificial intelligence and the mathematical theory of computation. Papers cover the logical approach to artificial intelligence; knowledge representation and common sense reasoning; automated deduction; logic programming; nonmonotonic reasoning and circumscription. One paper suggests that the design of parallel programming languages will invariably become more sophisticated as human skill in programming and software developments improves to attain faster running programs. An example of metaprogramming to systems concerns the design and control of operations of factory devices, such as robots and numerically controlled machine tools. Metaprogramming involves two design aspects: that of the activity of a single device and that of the interaction with other devices. One paper cites the application of artificial intelligence pertaining to the project "proof checker for first-order logic" at the Stanford Artificial Intelligence Laboratory. Another paper explains why the bisection algorithm widely used in computer science does not work. This book can prove valuable to engineers and researchers of electrical, computer, and mechanical engineering, as well as, for computer programmers and designers of industrial processes.