The Computational Complexity Of Algebraic And Numeric Problems
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The Computational Complexity Of Algebraic And Numeric Problems
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Author : Allan Borodin
language : en
Publisher: Elsevier Publishing Company
Release Date : 1975
The Computational Complexity Of Algebraic And Numeric Problems written by Allan Borodin and has been published by Elsevier Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
The Computational Complexity Of Algebraic And Numeric Problems
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Author : Allen Borodin
language : en
Publisher:
Release Date : 1988
The Computational Complexity Of Algebraic And Numeric Problems written by Allen Borodin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.
Algebraic Complexity Theory
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Author : Peter Bürgisser
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Algebraic Complexity Theory written by Peter Bürgisser and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under standing of the intrinsic computational difficulty of problems.
Applied Algebra Algebraic Algorithms And Error Correcting Codes
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Author : Gérard Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 1995
Applied Algebra Algebraic Algorithms And Error Correcting Codes written by Gérard Cohen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Algebra categories.
This book constitutes the proceedings of the 11th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-11, held in Paris, France in July 1995. The volume presents five invited papers and 32 full revised research papers selected from a total of 68 submissions; it is focussed on research directed to the exploitation of algebraic techniques and methodologies for the application in coding and computer algebra. Among the topics covered are coding, cryptoloy, communication, factorization of polynomials, Gröbner bases, computer algebra, algebraic algorithms, symbolic computation, algebraic manipulation.
Computational And Algorithmic Problems In Finite Fields
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Author : Igor Shparlinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computational And Algorithmic Problems In Finite Fields written by Igor Shparlinski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume presents an exhaustive treatment of computation and algorithms for finite fields. Topics covered include polynomial factorization, finding irreducible and primitive polynomials, distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types, and new applications of finite fields to other araes of mathematics. For completeness, also included are two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number generators, modular arithmetic etc.), and computational number theory (primality testing, factoring integers, computing in algebraic number theory, etc.) The problems considered here have many applications in computer science, coding theory, cryptography, number theory and discrete mathematics. The level of discussion presuppose only a knowledge of the basic facts on finite fields, and the book can be recommended as supplementary graduate text. For researchers and students interested in computational and algorithmic problems in finite fields.
Computational Complexity
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Author : Sanjeev Arora
language : en
Publisher: Cambridge University Press
Release Date : 2009-04-20
Computational Complexity written by Sanjeev Arora and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-20 with Computers categories.
This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set. The book starts with a broad introduction to the field and progresses to advanced results. Contents include: definition of Turing machines and basic time and space complexity classes, probabilistic algorithms, interactive proofs, cryptography, quantum computation, lower bounds for concrete computational models (decision trees, communication complexity, constant depth, algebraic and monotone circuits, proof complexity), average-case complexity and hardness amplification, derandomization and pseudorandom constructions, and the PCP theorem.
Modern Computer Algebra
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Author : Joachim von zur Gathen
language : en
Publisher: Cambridge University Press
Release Date : 2003-07-03
Modern Computer Algebra written by Joachim von zur Gathen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-03 with Computers categories.
Computer algebra systems are gaining importance in all areas of science and engineering. This textbook gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. It is designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics. Its comprehensiveness and authority also make it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). Some of this material has never appeared before in book form. For the new edition, errors have been corrected, the text has been smoothed and updated, and new sections on greatest common divisors and symbolic integration have been added.
Complexity Dichotomies For Counting Problems
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Author : Jin-Yi Cai
language : en
Publisher: Cambridge University Press
Release Date : 2017-11-16
Complexity Dichotomies For Counting Problems written by Jin-Yi Cai and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-16 with Computers categories.
Volume 1. Boolean domain
Applied Algebra Algebraic Algorithms And Error Correcting Codes
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Author :
language : en
Publisher:
Release Date : 1995
Applied Algebra Algebraic Algorithms And Error Correcting Codes written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Algebra categories.
Summary Of Awards
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Author :
language : en
Publisher:
Release Date :
Summary Of Awards written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Computers categories.