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Completeness And Reduction In Algebraic Complexity Theory
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Book Synopsis Completeness and Reduction in Algebraic Complexity Theory by : Peter Bürgisser
Download or read book Completeness and Reduction in Algebraic Complexity Theory written by Peter Bürgisser and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a thorough and comprehensive treatment of the theory of NP-completeness in the framework of algebraic complexity theory. Coverage includes Valiant's algebraic theory of NP-completeness; interrelations with the classical theory as well as the Blum-Shub-Smale model of computation, questions of structural complexity; fast evaluation of representations of general linear groups; and complexity of immanants.
Book Synopsis Algebraic Complexity Theory by : Peter Bürgisser
Download or read book Algebraic Complexity Theory written by Peter Bürgisser and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis P, NP, and NP-Completeness by : Oded Goldreich
Download or read book P, NP, and NP-Completeness written by Oded Goldreich and published by Cambridge University Press. This book was released on 2010-08-16 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this book is the P versus NP Question and the theory of NP-completeness. It also provides adequate preliminaries regarding computational problems and computational models. The P versus NP Question asks whether or not finding solutions is harder than checking the correctness of solutions. An alternative formulation asks whether or not discovering proofs is harder than verifying their correctness. It is widely believed that the answer to these equivalent formulations is positive, and this is captured by saying that P is different from NP. Although the P versus NP Question remains unresolved, the theory of NP-completeness offers evidence for the intractability of specific problems in NP by showing that they are universal for the entire class. Amazingly enough, NP-complete problems exist, and furthermore hundreds of natural computational problems arising in many different areas of mathematics and science are NP-complete.
Book Synopsis Computational Complexity by : Sanjeev Arora
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.
Book Synopsis Geometry and Complexity Theory by : J. M. Landsberg
Download or read book Geometry and Complexity Theory written by J. M. Landsberg and published by Cambridge University Press. This book was released on 2017-09-28 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two central problems in computer science are P vs NP and the complexity of matrix multiplication. The first is also a leading candidate for the greatest unsolved problem in mathematics. The second is of enormous practical and theoretical importance. Algebraic geometry and representation theory provide fertile ground for advancing work on these problems and others in complexity. This introduction to algebraic complexity theory for graduate students and researchers in computer science and mathematics features concrete examples that demonstrate the application of geometric techniques to real world problems. Written by a noted expert in the field, it offers numerous open questions to motivate future research. Complexity theory has rejuvenated classical geometric questions and brought different areas of mathematics together in new ways. This book will show the beautiful, interesting, and important questions that have arisen as a result.
Book Synopsis Computer Science – Theory and Applications by : Rahul Santhanam
Download or read book Computer Science – Theory and Applications written by Rahul Santhanam and published by Springer Nature. This book was released on 2021-06-16 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 16th International Computer Science Symposium in Russia, CSR 2021, held in Sochi, Russia, in June/July 2021. The 28 full papers were carefully reviewed and selected from 68 submissions. The papers cover a broad range of topics, such as formal languages and automata theory, geometry and discrete structures; theory and algorithms for application domains and much more.
Download or read book STACS 2007 written by Wolfgang Thomas and published by Springer Science & Business Media. This book was released on 2007-02-08 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 24th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2007, held in Aachen, Germany in February 2007. The 56 revised full papers presented together with 3 invited papers were carefully reviewed and selected from about 400 submissions. The papers address the whole range of theoretical computer science including algorithms and data structures, automata and formal languages, complexity theory, logic in computer science, semantics, specification, and verification of programs, rewriting and deduction, as well as current challenges like biological computing, quantum computing, and mobile and net computing.
Book Synopsis Algorithms and Computation by : Leizhen Cai
Download or read book Algorithms and Computation written by Leizhen Cai and published by Springer. This book was released on 2013-12-12 with total page 761 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 24th International Symposium on Algorithms and Computation, ISAAC 2013, held in Hong Kong, China in December 2013. The 67 revised full papers presented together with 2 invited talks were carefully reviewed and selected from 177 submissions for inclusion in the book. The focus of the volume in on the following topics: computation geometry, pattern matching, computational complexity, internet and social network algorithms, graph theory and algorithms, scheduling algorithms, fixed-parameter tractable algorithms, algorithms and data structures, algorithmic game theory, approximation algorithms and network algorithms.
Book Synopsis Open Problems in Algebraic Combinatorics by : Christine Berkesch
Download or read book Open Problems in Algebraic Combinatorics written by Christine Berkesch and published by American Mathematical Society. This book was released on 2024-08-21 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: In their preface, the editors describe algebraic combinatorics as the area of combinatorics concerned with exact, as opposed to approximate, results and which puts emphasis on interaction with other areas of mathematics, such as algebra, topology, geometry, and physics. It is a vibrant area, which saw several major developments in recent years. The goal of the 2022 conference Open Problems in Algebraic Combinatorics 2022 was to provide a forum for exchanging promising new directions and ideas. The current volume includes contributions coming from the talks at the conference, as well as a few other contributions written specifically for this volume. The articles cover the majority of topics in algebraic combinatorics with the aim of presenting recent important research results and also important open problems and conjectures encountered in this research. The editors hope that this book will facilitate the exchange of ideas in algebraic combinatorics.
Book Synopsis Recent Advances in Real Complexity and Computation by : Luis M. Pardo
Download or read book Recent Advances in Real Complexity and Computation written by Luis M. Pardo and published by American Mathematical Soc.. This book was released on 2014-11-12 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is composed of six contributions derived from the lectures given during the UIMP-RSME Lluis Santalo Summer School on ``Recent Advances in Real Complexity and Computation'', held July 16-20, 2012, in Santander, Spain. The goal of this Summer School was to present some of the recent advances on Smale's 17th Problem: ``Can a zero of $n$ complex polynomial equations in $n$ unknowns be found approximately, on the average, in polynomial time with a uniform algorithm?'' These papers cover several aspects of this problem: from numerical to symbolic methods in polynomial equation solving, computational complexity aspects (both worse and average cases and both upper and lower complexity bounds) as well as aspects of the underlying geometry of the problem. Some of the contributions also deal with either real or multiple solutions solving.
Book Synopsis Computing and Combinatorics by : Ding-Zhu Du
Download or read book Computing and Combinatorics written by Ding-Zhu Du and published by Springer. This book was released on 2019-07-24 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 25th International Conference on Computing and Combinatorics, COCOON 2019, held in Xi’an, China, in July 2019. The 55 papers presented in this volume were carefully reviewed and selected from 124 submissions. The papers cover various topics, including algorithm design, approximation algorithm, graph theory, complexity theory, problem solving, optimization, computational biology, computational learning, communication network, logic, and game theory.
Book Synopsis Perspectives in Computational Complexity by : Manindra Agrawal
Download or read book Perspectives in Computational Complexity written by Manindra Agrawal and published by Springer. This book was released on 2014-07-16 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together contributions by leading researchers in computational complexity theory written in honor of Somenath Biswas on the occasion of his sixtieth birthday. They discuss current trends and exciting developments in this flourishing area of research and offer fresh perspectives on various aspects of complexity theory. The topics covered include arithmetic circuit complexity, lower bounds and polynomial identity testing, the isomorphism conjecture, space-bounded computation, graph isomorphism, resolution and proof complexity, entropy and randomness. Several chapters have a tutorial flavor. The aim is to make recent research in these topics accessible to graduate students and senior undergraduates in computer science and mathematics. It can also be useful as a resource for teaching advanced level courses in computational complexity.
Book Synopsis Mathematical Foundations of Computer Science 2013 by : Krishnendu Chatterjee
Download or read book Mathematical Foundations of Computer Science 2013 written by Krishnendu Chatterjee and published by Springer. This book was released on 2013-08-16 with total page 869 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed conference proceedings of the 38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013, held in Klosterneuburg, Austria, in August 2013. The 67 revised full papers presented together with six invited talks were carefully selected from 191 submissions. Topics covered include algorithmic game theory, algorithmic learning theory, algorithms and data structures, automata, formal languages, bioinformatics, complexity, computational geometry, computer-assisted reasoning, concurrency theory, databases and knowledge-based systems, foundations of computing, logic in computer science, models of computation, semantics and verification of programs, and theoretical issues in artificial intelligence.
Book Synopsis Logical Approaches to Computational Barriers by : Arnold Beckmann
Download or read book Logical Approaches to Computational Barriers written by Arnold Beckmann and published by Springer Science & Business Media. This book was released on 2006-06-26 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second International Conference on Computability in Europe, CiE 2006, held in Swansea, UK, June/July 2006. The book presents 31 revised full papers together with 30 invited papers, including papers corresponding to 8 plenary talks and 6 special sessions on proofs and computation, computable analysis, challenges in complexity, foundations of programming, mathematical models of computers and hypercomputers, and Gödel centenary: Gödel's legacy for computability.
Book Synopsis Fundamentals of Computation Theory by : Witold Charatonik
Download or read book Fundamentals of Computation Theory written by Witold Charatonik and published by Springer Science & Business Media. This book was released on 2009-07-28 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 17th International Symposium Fundamentals of Computation Theory, FCT 2009, held in Wroclaw, Poland in August 2009. The 29 revised full papers were carefully reviewed and selected from 67 submissions. The papers address all current topics in computation theory such as automata and formal languages, design and analysis of algorithms, computational and structural complexity, semantics, logic, algebra and categories in computer science, circuits and networks, learning theory, specification and verification, parallel and distributed systems, concurrency theory, cryptography and cryptograhic protocols, approximation and randomized algorithms, computational geometry, quantum computation and information, bio-inspired computation.
Book Synopsis Mathematical Foundations of Computer Science 2007 by : Ludek Kucera
Download or read book Mathematical Foundations of Computer Science 2007 written by Ludek Kucera and published by Springer. This book was released on 2007-08-15 with total page 779 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 32nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2007, held in Ceský Krumlov, Czech Republic, August 2007. The 61 revised full papers presented together with the full papers or abstracts of five invited talks address all current aspects in theoretical computer science and its mathematical foundations.
Author :European Association for Computer Science Logic. Conference Publisher :Springer Science & Business Media ISBN 13 :3540678956 Total Pages :556 pages Book Rating :4.5/5 (46 download)
Book Synopsis Computer Science Logic by : European Association for Computer Science Logic. Conference
Download or read book Computer Science Logic written by European Association for Computer Science Logic. Conference and published by Springer Science & Business Media. This book was released on 2000-08-09 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 13th International Workshop on Computer Science Logic, CSL 2000, held in Fischbachau, Germany as the 8th Annual Conference of the EACSL in August 2000. The 28 revised full papers presented together with eight invited papers were carefully reviewed and selected by the program committee. Among the topics covered are automated deduction, theorem proving, categorical logic, term rewriting, finite model theory, higher order logic, lambda and combinatory calculi, computational complexity, logic programing, constraints, linear logic, modal logic, temporal logic, model checking, formal specification, formal verification, program transformation, etc.
