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Introduction To Circuit Complexity
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Book Synopsis Introduction to Circuit Complexity by : Heribert Vollmer
Download or read book Introduction to Circuit Complexity written by Heribert Vollmer and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: An advanced textbook giving a broad, modern view of the computational complexity theory of boolean circuits, with extensive references, for theoretical computer scientists and mathematicians.
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 The Complexity of Boolean Functions by : Ingo Wegener
Download or read book The Complexity of Boolean Functions written by Ingo Wegener and published by . This book was released on 1987 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to the Theory of Complexity by : Daniel Pierre Bovet
Download or read book Introduction to the Theory of Complexity written by Daniel Pierre Bovet and published by Prentice Hall PTR. This book was released on 1994 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using a balanced approach that is partly algorithmic and partly structuralist, this book systematically reviews the most significant results obtained in the study of computational complexity theory. Features over 120 worked examples, over 200 problems, and 400 figures.
Book Synopsis Arithmetic Circuits by : Amir Shpilka
Download or read book Arithmetic Circuits written by Amir Shpilka and published by Now Publishers Inc. This book was released on 2010 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: A large class of problems in symbolic computation can be expressed as the task of computing some polynomials; and arithmetic circuits form the most standard model for studying the complexity of such computations. This algebraic model of computation attracted a large amount of research in the last five decades, partially due to its simplicity and elegance. Being a more structured model than Boolean circuits, one could hope that the fundamental problems of theoretical computer science, such as separating P from NP, will be easier to solve for arithmetic circuits. However, in spite of the appearing simplicity and the vast amount of mathematical tools available, no major breakthrough has been seen. In fact, all the fundamental questions are still open for this model as well. Nevertheless, there has been a lot of progress in the area and beautiful results have been found, some in the last few years. As examples we mention the connection between polynomial identity testing and lower bounds of Kabanets and Impagliazzo, the lower bounds of Raz for multilinear formulas, and two new approaches for proving lower bounds: Geometric Complexity Theory and Elusive Functions. The goal of this monograph is to survey the field of arithmetic circuit complexity, focusing mainly on what we find to be the most interesting and accessible research directions. We aim to cover the main results and techniques, with an emphasis on works from the last two decades. In particular, we discuss the recent lower bounds for multilinear circuits and formulas, the advances in the question of deterministically checking polynomial identities, and the results regarding reconstruction of arithmetic circuits. We do, however, also cover part of the classical works on arithmetic circuits. In order to keep this monograph at a reasonable length, we do not give full proofs of most theorems, but rather try to convey the main ideas behind each proof and demonstrate it, where possible, by proving some special cases.
Book Synopsis Boolean Functions and Computation Models by : Peter Clote
Download or read book Boolean Functions and Computation Models written by Peter Clote and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two internationally renowned authors elucidate the structure of "fast" parallel computation. Its complexity is emphasised through a variety of techniques ranging from finite combinatorics, probability theory and finite group theory to finite model theory and proof theory. Non-uniform computation models are studied in the form of Boolean circuits; uniform ones in a variety of forms. Steps in the investigation of non-deterministic polynomial time are surveyed as is the complexity of various proof systems. Providing a survey of research in the field, the book will benefit advanced undergraduates and graduate students as well as researchers.
Book Synopsis Introduction to Quantum Algorithms by : Johannes A. Buchmann
Download or read book Introduction to Quantum Algorithms written by Johannes A. Buchmann and published by American Mathematical Society. This book was released on 2024-03-18 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum algorithms are among the most important, interesting, and promising innovations in information and communication technology. They pose a major threat to today's cybersecurity and at the same time promise great benefits by potentially solving previously intractable computational problems with reasonable effort. The theory of quantum algorithms is based on advanced concepts from computer science, mathematics, and physics. Introduction to Quantum Algorithms offers a mathematically precise exploration of these concepts, accessible to those with a basic mathematical university education, while also catering to more experienced readers. This comprehensive book is suitable for self-study or as a textbook for one- or two-semester introductory courses on quantum computing algorithms. Instructors can tailor their approach to emphasize theoretical understanding and proofs or practical applications of quantum algorithms, depending on the course's goals and timeframe.
Book Synopsis Theory of Computational Complexity by : Ding-Zhu Du
Download or read book Theory of Computational Complexity written by Ding-Zhu Du and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete treatment of fundamentals and recent advances in complexity theory Complexity theory studies the inherent difficulties of solving algorithmic problems by digital computers. This comprehensive work discusses the major topics in complexity theory, including fundamental topics as well as recent breakthroughs not previously available in book form. Theory of Computational Complexity offers a thorough presentation of the fundamentals of complexity theory, including NP-completeness theory, the polynomial-time hierarchy, relativization, and the application to cryptography. It also examines the theory of nonuniform computational complexity, including the computational models of decision trees and Boolean circuits, and the notion of polynomial-time isomorphism. The theory of probabilistic complexity, which studies complexity issues related to randomized computation as well as interactive proof systems and probabilistically checkable proofs, is also covered. Extraordinary in both its breadth and depth, this volume: * Provides complete proofs of recent breakthroughs in complexity theory * Presents results in well-defined form with complete proofs and numerous exercises * Includes scores of graphs and figures to clarify difficult material An invaluable resource for researchers as well as an important guide for graduate and advanced undergraduate students, Theory of Computational Complexity is destined to become the standard reference in the field.
Book Synopsis Computational Complexity by : Oded Goldreich
Download or read book Computational Complexity written by Oded Goldreich and published by Cambridge University Press. This book was released on 2008-04-28 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive perspective to modern topics in complexity theory, which is a central field of the theoretical foundations of computer science. It addresses the looming question of what can be achieved within a limited amount of time with or without other limited natural computational resources. Can be used as an introduction for advanced undergraduate and graduate students as either a textbook or for self-study, or to experts, since it provides expositions of the various sub-areas of complexity theory such as hardness amplification, pseudorandomness and probabilistic proof systems.
Book Synopsis Proof Complexity and Feasible Arithmetics by : Paul W. Beame
Download or read book Proof Complexity and Feasible Arithmetics written by Paul W. Beame and published by American Mathematical Soc.. This book was released on with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Questions of mathematical proof and logical inference have been a significant thread in modern mathematics and have played a formative role in the development of computer science and artificial intelligence. Research in proof complexity and feasible theories of arithmetic aims at understanding not only whether or not logical inferences can be made but also what resources are required to carry them out. Understanding the resources required for logical inferences has major implications for some of the most important problems in computational complexity, particularly the problem of whether or not NP is equal to co-NP. In addition, these have important implications for the efficiency of automated reasoning systems. The last dozen years have seen several breakthroughs in the study of these resource requirement. Papers in this volume represent the proceedings of the DIMACS workshop on "Feasible Arithmetics and Proof Complexity" held in April 1996 in Rutgers, NJ, as part of the DIMACS Institute's Special Year on Logic and Algorithms. This book brings together some of the most recent work of leading researchers in proof complexity and feasible arithmetic reflecting many of these advances. It covers a number of aspects of the field including lower bounds in proof complexity, witnessing theorems and proof systems for feasible arithmetic, algebraic and combinatorial proof systems, interpolation theorems, and the relationship between proof complexity and Boolean circuit complexity.
Download or read book STACS 2006 written by Bruno Durand and published by Springer Science & Business Media. This book was released on 2006-02-14 with total page 730 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 23rd Annual Symposium on Theoretical Aspects of Computer Science, held in February 2006. The 54 revised full papers presented together with three invited papers were carefully reviewed and selected from 283 submissions. The papers address the whole range of theoretical computer science including algorithms and data structures, automata and formal languages, complexity theory, semantics, and logic in computer science.
Book Synopsis Circuit Complexity and Neural Networks by : Ian Parberry
Download or read book Circuit Complexity and Neural Networks written by Ian Parberry and published by MIT Press. This book was released on 1994 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neural networks usually work adequately on small problems but can run into trouble when they are scaled up to problems involving large amounts of input data. Circuit Complexity and Neural Networks addresses the important question of how well neural networks scale - that is, how fast the computation time and number of neurons grow as the problem size increases. It surveys recent research in circuit complexity (a robust branch of theoretical computer science) and applies this work to a theoretical understanding of the problem of scalability. Most research in neural networks focuses on learning, yet it is important to understand the physical limitations of the network before the resources needed to solve a certain problem can be calculated. One of the aims of this book is to compare the complexity of neural networks and the complexity of conventional computers, looking at the computational ability and resources (neurons and time) that are a necessary part of the foundations of neural network learning. Circuit Complexity and Neural Networks contains a significant amount of background material on conventional complexity theory that will enable neural network scientists to learn about how complexity theory applies to their discipline, and allow complexity theorists to see how their discipline applies to neural networks.
Book Synopsis An Introduction to Kolmogorov Complexity and Its Applications by : Ming Li
Download or read book An Introduction to Kolmogorov Complexity and Its Applications written by Ming Li and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).
Book Synopsis Integrated Circuit Design and Technology by : M. J. Morant
Download or read book Integrated Circuit Design and Technology written by M. J. Morant and published by Springer. This book was released on 2013-12-01 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Rewriting Techniques and Applications by : Aart Middeldorp
Download or read book Rewriting Techniques and Applications written by Aart Middeldorp and published by Springer. This book was released on 2003-06-29 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th International Conference on Rewriting Techniques and Applications, RTA 2001, held in Utrecht, The Netherlands, in May 2001. The 23 revised full papers presented together with two system descriptions were carefully reviewed and selected from 55 submissions. All current aspects of rewriting are addressed.
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 Language and Automata Theory and Applications by : Adrian-Horia Dediu
Download or read book Language and Automata Theory and Applications written by Adrian-Horia Dediu and published by Springer. This book was released on 2016-02-29 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 10th International Conference on Language and Automata Theory and Applications, LATA 2016, held in Prague, Czech Republic, in March 2016. The 42 revised full papers presented together with 5 invited talks were carefully reviewed and selected from 119 submissions. The papers cover the following topics: algebraic language theory; algorithms for semi-structured data mining, algorithms on automata and words; automata and logic; automata for system analysis and program verification; automata networks, concurrency and Petri nets; automatic structures; cellular automata, codes, combinatorics on words; computational complexity; data and image compression; descriptional complexity; digital libraries and document engineering; foundations of finite state technology; foundations of XML; fuzzy and rough languages; grammatical inference and algorithmic learning; graphs and graph transformation; language varieties and semigroups; parallel and regulated rewriting; parsing; patterns; string and combinatorial issues in computational biology and bioinformatics; string processing algorithms; symbolic dynamics; term rewriting; transducers; trees, tree languages and tree automata; weighted automata.
