Computability Complexity And Languages

Author : Martin D. Davis
Publisher : Academic Press
ISBN 13 : 1483264580
Total Pages : 448 pages
Book Rating : 4.85/5 ( download)

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Download or read book Computability, Complexity, and Languages written by Martin D. Davis and published by Academic Press. This book was released on 2014-05-10 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computability, Complexity, and Languages: Fundamentals of Theoretical Computer Science provides an introduction to the various aspects of theoretical computer science. Theoretical computer science is the mathematical study of models of computation. This text is composed of five parts encompassing 17 chapters, and begins with an introduction to the use of proofs in mathematics and the development of computability theory in the context of an extremely simple abstract programming language. The succeeding parts demonstrate the performance of abstract programming language using a macro expansion technique, along with presentations of the regular and context-free languages. Other parts deal with the aspects of logic that are important for computer science and the important theory of computational complexity, as well as the theory of NP-completeness. The closing part introduces the advanced recursion and polynomial-time computability theories, including the priority constructions for recursively enumerable Turing degrees. This book is intended primarily for undergraduate and graduate mathematics students.

Author : Martin Davis
Publisher : Academic Press
ISBN 13 : 0122063821
Total Pages : 631 pages
Book Rating : 4.24/5 ( download)

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Download or read book Computability, Complexity, and Languages written by Martin Davis and published by Academic Press. This book was released on 1994-02-03 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory text covers the key areas of computer science, including recursive function theory, formal languages, and automata. Additions to the second edition include: extended exercise sets, which vary in difficulty; expanded section on recursion theory; new chapters on program verification and logic programming; updated references and examples throughout.

Author : Neil D. Jones
Publisher : MIT Press
ISBN 13 : 9780262100649
Total Pages : 494 pages
Book Rating : 4.49/5 ( download)

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Download or read book Computability and Complexity written by Neil D. Jones and published by MIT Press. This book was released on 1997 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computability and complexity theory should be of central concern to practitioners as well as theorists. Unfortunately, however, the field is known for its impenetrability. Neil Jones's goal as an educator and author is to build a bridge between computability and complexity theory and other areas of computer science, especially programming. In a shift away from the Turing machine- and G�del number-oriented classical approaches, Jones uses concepts familiar from programming languages to make computability and complexity more accessible to computer scientists and more applicable to practical programming problems. According to Jones, the fields of computability and complexity theory, as well as programming languages and semantics, have a great deal to offer each other. Computability and complexity theory have a breadth, depth, and generality not often seen in programming languages. The programming language community, meanwhile, has a firm grasp of algorithm design, presentation, and implementation. In addition, programming languages sometimes provide computational models that are more realistic in certain crucial aspects than traditional models. New results in the book include a proof that constant time factors do matter for its programming-oriented model of computation. (In contrast, Turing machines have a counterintuitive "constant speedup" property: that almost any program can be made to run faster, by any amount. Its proof involves techniques irrelevant to practice.) Further results include simple characterizations in programming terms of the central complexity classes PTIME and LOGSPACE, and a new approach to complete problems for NLOGSPACE, PTIME, NPTIME, and PSPACE, uniformly based on Boolean programs. Foundations of Computing series

Author : Steven Homer
Publisher : Springer Science & Business Media
ISBN 13 : 1461406811
Total Pages : 310 pages
Book Rating : 4.15/5 ( download)

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Download or read book Computability and Complexity Theory written by Steven Homer and published by Springer Science & Business Media. This book was released on 2011-12-09 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and extensively expanded edition of Computability and Complexity Theory comprises essential materials that are core knowledge in the theory of computation. The book is self-contained, with a preliminary chapter describing key mathematical concepts and notations. Subsequent chapters move from the qualitative aspects of classical computability theory to the quantitative aspects of complexity theory. Dedicated chapters on undecidability, NP-completeness, and relative computability focus on the limitations of computability and the distinctions between feasible and intractable. Substantial new content in this edition includes: a chapter on nonuniformity studying Boolean circuits, advice classes and the important result of Karp─Lipton. a chapter studying properties of the fundamental probabilistic complexity classes a study of the alternating Turing machine and uniform circuit classes. an introduction of counting classes, proving the famous results of Valiant and Vazirani and of Toda a thorough treatment of the proof that IP is identical to PSPACE With its accessibility and well-devised organization, this text/reference is an excellent resource and guide for those looking to develop a solid grounding in the theory of computing. Beginning graduates, advanced undergraduates, and professionals involved in theoretical computer science, complexity theory, and computability will find the book an essential and practical learning tool. Topics and features: Concise, focused materials cover the most fundamental concepts and results in the field of modern complexity theory, including the theory of NP-completeness, NP-hardness, the polynomial hierarchy, and complete problems for other complexity classes Contains information that otherwise exists only in research literature and presents it in a unified, simplified manner Provides key mathematical background information, including sections on logic and number theory and algebra Supported by numerous exercises and supplementary problems for reinforcement and self-study purposes

Author : Elaine Rich
Publisher : Prentice Hall
ISBN 13 : 0132288060
Total Pages : 1120 pages
Book Rating : 4.64/5 ( download)

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Download or read book Automata, Computability and Complexity written by Elaine Rich and published by Prentice Hall. This book was released on 2008 with total page 1120 pages. Available in PDF, EPUB and Kindle. Book excerpt: For upper level courses on Automata. Combining classic theory with unique applications, this crisp narrative is supported by abundant examples and clarifies key concepts by introducing important uses of techniques in real systems. Broad-ranging coverage allows instructors to easily customise course material to fit their unique requirements.

Author : E. Börger
Publisher : North Holland
ISBN 13 :
Total Pages : 630 pages
Book Rating : 4.46/5 ( download)

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Download or read book Computability, Complexity, Logic written by E. Börger and published by North Holland. This book was released on 1989-07 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theme of this book is formed by a pair of concepts: the concept of formal language as carrier of the precise expression of meaning, facts and problems, and the concept of algorithm or calculus, i.e. a formally operating procedure for the solution of precisely described questions and problems. The book is a unified introduction to the modern theory of these concepts, to the way in which they developed first in mathematical logic and computability theory and later in automata theory, and to the theory of formal languages and complexity theory. Apart from considering the fundamental themes and classical aspects of these areas, the subject matter has been selected to give priority throughout to the new aspects of traditional questions, results and methods which have developed from the needs or knowledge of computer science and particularly of complexity theory. It is both a textbook for introductory courses in the above-mentioned disciplines as well as a monograph in which further results of new research are systematically presented and where an attempt is made to make explicit the connections and analogies between a variety of concepts and constructions.

Author : Dexter C. Kozen
Publisher : Springer
ISBN 13 : 364285706X
Total Pages : 399 pages
Book Rating : 4.65/5 ( download)

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Download or read book Automata and Computability written by Dexter C. Kozen and published by Springer. This book was released on 2013-11-11 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are my lecture notes from CS381/481: Automata and Computability Theory, a one-semester senior-level course I have taught at Cornell Uni versity for many years. I took this course myself in thc fall of 1974 as a first-year Ph.D. student at Cornell from Juris Hartmanis and have been in love with the subject ever sin,:e. The course is required for computer science majors at Cornell. It exists in two forms: CS481, an honors version; and CS381, a somewhat gentler paced version. The syllabus is roughly the same, but CS481 go es deeper into thc subject, covers more material, and is taught at a more abstract level. Students are encouraged to start off in one or the other, then switch within the first few weeks if they find the other version more suitaLle to their level of mathematical skill. The purpose of t.hc course is twofold: to introduce computer science students to the rieh heritage of models and abstractions that have arisen over the years; and to dew!c'p the capacity to form abstractions of their own and reason in terms of them.

Author : Lenore Blum
Publisher : Springer Science & Business Media
ISBN 13 : 1461207010
Total Pages : 456 pages
Book Rating : 4.16/5 ( download)

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Download or read book Complexity and Real Computation written by Lenore Blum and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical theory of computation has its origins in the work of Goedel, Turing, Church, and Kleene and has been an extraordinarily successful framework for theoretical computer science. The thesis of this book, however, is that it provides an inadequate foundation for modern scientific computation where most of the algorithms are real number algorithms. The goal of this book is to develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing. Along the way, the authors consider such fundamental problems as: * Is the Mandelbrot set decidable? * For simple quadratic maps, is the Julia set a halting set? * What is the real complexity of Newton's method? * Is there an algorithm for deciding the knapsack problem in a ploynomial number of steps? * Is the Hilbert Nullstellensatz intractable? * Is the problem of locating a real zero of a degree four polynomial intractable? * Is linear programming tractable over the reals? The book is divided into three parts: The first part provides an extensive introduction and then proves the fundamental NP-completeness theorems of Cook-Karp and their extensions to more general number fields as the real and complex numbers. The later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing.

Author : Sanjeev Arora
Publisher : Cambridge University Press
ISBN 13 : 0521424267
Total Pages : 609 pages
Book Rating : 4.64/5 ( download)

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Download or read book Computational Complexity written by Sanjeev Arora and published by Cambridge University Press. This book was released on 2009-04-20 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Author : Alan P. Parkes
Publisher : Springer Science & Business Media
ISBN 13 : 144710143X
Total Pages : 352 pages
Book Rating : 4.37/5 ( download)

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Download or read book Introduction to Languages, Machines and Logic written by Alan P. Parkes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: A well-written and accessible introduction to the most important features of formal languages and automata theory. It focuses on the key concepts, illustrating potentially intimidating material through diagrams and pictorial representations, and this edition includes new and expanded coverage of topics such as: reduction and simplification of material on Turing machines; complexity and O notation; propositional logic and first order predicate logic. Aimed primarily at computer scientists rather than mathematicians, algorithms and proofs are presented informally through examples, and there are numerous exercises (many with solutions) and an extensive glossary.