Computability And Complexity Theory

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Computability and Complexity Theory

Steven Homer,Alan L. Selman
Computability and Complexity Theory Book PDF

Author : Steven Homer,Alan L. Selman
Publisher : Springer Science & Business Media
Page : 310 pages
File Size : 43,7 Mb
Release : 2011-12-09
Category : Computers
ISBN : 9781461406815

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Computability and Complexity Theory by Steven Homer,Alan L. Selman Pdf

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

Computability and Complexity Theory

Steven Homer,Alan L. Selman
Computability and Complexity Theory Book PDF

Author : Steven Homer,Alan L. Selman
Publisher : Springer Science & Business Media
Page : 206 pages
File Size : 49,7 Mb
Release : 2013-03-09
Category : Computers
ISBN : 9781475735444

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Computability and Complexity Theory by Steven Homer,Alan L. Selman Pdf

Intended for use in an introductory graduate course in theoretical computer science, this text contains material that should be core knowledge in the theory of computation for all graduates in computer science. It is self-contained and is best suited for a one semester course. The text starts with classical computability theory which forms the basis for complexity theory. This has the pedagogical advantage that students learn a qualitative subject before advancing to a quantitative one. Since this is a graduate course, students should have some knowledge of such topics as automata theory, formal languages, computability theory, or complexity theory.

Computability and Complexity

Neil D. Jones
Computability and Complexity Book PDF

Author : Neil D. Jones
Publisher : MIT Press
Page : 494 pages
File Size : 55,9 Mb
Release : 1997
Category : Computers
ISBN : 0262100649

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Computability and Complexity by Neil D. Jones Pdf

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

Automata, Computability and Complexity

Elaine Rich
Automata Computability and Complexity Book PDF

Author : Elaine Rich
Publisher : Prentice Hall
Page : 1120 pages
File Size : 54,8 Mb
Release : 2008
Category : Computers
ISBN : 9780132288064

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Automata, Computability and Complexity by Elaine Rich Pdf

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.

Computability, Complexity, and Languages

Martin Davis,Ron Sigal,Elaine J. Weyuker
Computability Complexity and Languages Book PDF

Author : Martin Davis,Ron Sigal,Elaine J. Weyuker
Publisher : Academic Press
Page : 631 pages
File Size : 40,5 Mb
Release : 1994-02-03
Category : Computers
ISBN : 9780122063824

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Computability, Complexity, and Languages by Martin Davis,Ron Sigal,Elaine J. Weyuker Pdf

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.

Computational Complexity

Sanjeev Arora,Boaz Barak
Computational Complexity Book PDF

Author : Sanjeev Arora,Boaz Barak
Publisher : Cambridge University Press
Page : 609 pages
File Size : 48,8 Mb
Release : 2009-04-20
Category : Computers
ISBN : 9780521424264

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Computational Complexity by Sanjeev Arora,Boaz Barak Pdf

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Computability, Complexity, and Languages

Martin D. Davis,Elaine J. Weyuker
Computability Complexity and Languages Book PDF

Author : Martin D. Davis,Elaine J. Weyuker
Publisher : Academic Press
Page : 446 pages
File Size : 44,9 Mb
Release : 2014-05-10
Category : Reference
ISBN : 9781483264585

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Computability, Complexity, and Languages by Martin D. Davis,Elaine J. Weyuker Pdf

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.

Complexity and Real Computation

Lenore Blum,Felipe Cucker,Michael Shub,Steve Smale
Complexity and Real Computation Book PDF

Author : Lenore Blum,Felipe Cucker,Michael Shub,Steve Smale
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461207016

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Complexity and Real Computation by Lenore Blum,Felipe Cucker,Michael Shub,Steve Smale Pdf

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.

Handbook of Computability and Complexity in Analysis

Vasco Brattka,Peter Hertling
Handbook of Computability and Complexity in Analysis Book PDF

Author : Vasco Brattka,Peter Hertling
Publisher : Springer Nature
Page : 427 pages
File Size : 45,6 Mb
Release : 2021-06-04
Category : Computers
ISBN : 9783030592349

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Handbook of Computability and Complexity in Analysis by Vasco Brattka,Peter Hertling Pdf

Computable analysis is the modern theory of computability and complexity in analysis that arose out of Turing's seminal work in the 1930s. This was motivated by questions such as: which real numbers and real number functions are computable, and which mathematical tasks in analysis can be solved by algorithmic means? Nowadays this theory has many different facets that embrace topics from computability theory, algorithmic randomness, computational complexity, dynamical systems, fractals, and analog computers, up to logic, descriptive set theory, constructivism, and reverse mathematics. In recent decades computable analysis has invaded many branches of analysis, and researchers have studied computability and complexity questions arising from real and complex analysis, functional analysis, and the theory of differential equations, up to (geometric) measure theory and topology. This handbook represents the first coherent cross-section through most active research topics on the more theoretical side of the field. It contains 11 chapters grouped into parts on computability in analysis; complexity, dynamics, and randomness; and constructivity, logic, and descriptive complexity. All chapters are written by leading experts working at the cutting edge of the respective topic. Researchers and graduate students in the areas of theoretical computer science and mathematical logic will find systematic introductions into many branches of computable analysis, and a wealth of information and references that will help them to navigate the modern research literature in this field.

Theoretical Computer Science

Juraj Hromkovič
Theoretical Computer Science Book PDF

Author : Juraj Hromkovič
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 47,6 Mb
Release : 2003-09-18
Category : Computers
ISBN : 3540140158

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Theoretical Computer Science by Juraj Hromkovič Pdf

Juraj Hromkovic takes the reader on an elegant route through the theoretical fundamentals of computer science. The author shows that theoretical computer science is a fascinating discipline, full of spectacular contributions and miracles. The book also presents the development of the computer scientist's way of thinking as well as fundamental concepts such as approximation and randomization in algorithmics, and the basic ideas of cryptography and interconnection network design.

Computability, Complexity, Logic

E. Börger
Computability Complexity Logic Book PDF

Author : E. Börger
Publisher : Elsevier
Page : 591 pages
File Size : 40,8 Mb
Release : 1989-07-01
Category : Mathematics
ISBN : 008088704X

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Computability, Complexity, Logic by E. Börger Pdf

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.

Algorithmic Randomness and Complexity

Rodney G. Downey,Denis R. Hirschfeldt
Algorithmic Randomness and Complexity Book PDF

Author : Rodney G. Downey,Denis R. Hirschfeldt
Publisher : Springer Science & Business Media
Page : 855 pages
File Size : 44,9 Mb
Release : 2010-10-29
Category : Computers
ISBN : 9780387684413

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Algorithmic Randomness and Complexity by Rodney G. Downey,Denis R. Hirschfeldt Pdf

Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.

Computable Analysis

Klaus Weihrauch
Computable Analysis Book PDF

Author : Klaus Weihrauch
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 41,5 Mb
Release : 2000-09-14
Category : Computers
ISBN : 3540668179

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Computable Analysis by Klaus Weihrauch Pdf

Merging fundamental concepts of analysis and recursion theory to a new exciting theory, this book provides a solid fundament for studying various aspects of computability and complexity in analysis. It is the result of an introductory course given for several years and is written in a style suitable for graduate-level and senior students in computer science and mathematics. Many examples illustrate the new concepts while numerous exercises of varying difficulty extend the material and stimulate readers to work actively on the text.

Complexity Theory of Real Functions

K. Ko
Complexity Theory of Real Functions Book PDF

Author : K. Ko
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781468468021

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Complexity Theory of Real Functions by K. Ko Pdf

Starting with Cook's pioneering work on NP-completeness in 1970, polynomial complexity theory, the study of polynomial-time com putability, has quickly emerged as the new foundation of algorithms. On the one hand, it bridges the gap between the abstract approach of recursive function theory and the concrete approach of analysis of algorithms. It extends the notions and tools of the theory of computability to provide a solid theoretical foundation for the study of computational complexity of practical problems. In addition, the theoretical studies of the notion of polynomial-time tractability some times also yield interesting new practical algorithms. A typical exam ple is the application of the ellipsoid algorithm to combinatorial op timization problems (see, for example, Lovasz [1986]). On the other hand, it has a strong influence on many different branches of mathe matics, including combinatorial optimization, graph theory, number theory and cryptography. As a consequence, many researchers have begun to re-examine various branches of classical mathematics from the complexity point of view. For a given nonconstructive existence theorem in classical mathematics, one would like to find a construc tive proof which admits a polynomial-time algorithm for the solution. One of the examples is the recent work on algorithmic theory of per mutation groups. In the area of numerical computation, there are also two tradi tionally independent approaches: recursive analysis and numerical analysis.

Introduction to the Theory of Computation

Michael Sipser
Introduction to the Theory of Computation Book PDF

Author : Michael Sipser
Publisher : Thomson/Course Technology
Page : 437 pages
File Size : 42,7 Mb
Release : 2006
Category : Computational complexity
ISBN : 0619217642

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Introduction to the Theory of Computation by Michael Sipser Pdf

"Intended as an upper-level undergraduate or introductory graduate text in computer science theory," this book lucidly covers the key concepts and theorems of the theory of computation. The presentation is remarkably clear; for example, the "proof idea," which offers the reader an intuitive feel for how the proof was constructed, accompanies many of the theorems and a proof. Introduction to the Theory of Computation covers the usual topics for this type of text plus it features a solid section on complexity theory--including an entire chapter on space complexity. The final chapter introduces more advanced topics, such as the discussion of complexity classes associated with probabilistic algorithms.