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Author : H. J. Hoover
Publisher :
ISBN 13 :
Total Pages : 49 pages
Book Rating : 4.:/5 (159 download)
Download or read book Some Topics in Circuit Complexity written by H. J. Hoover and published by . This book was released on 1979 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Heribert Vollmer
Publisher : Springer Science & Business Media
ISBN 13 : 3662039273
Total Pages : 277 pages
Book Rating : 4.6/5 (62 download)
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.
Author : Sanjeev Arora
Publisher : Cambridge University Press
ISBN 13 : 0521424267
Total Pages : 609 pages
Book Rating : 4.5/5 (214 download)
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 : Ian Parberry
Publisher : MIT Press
ISBN 13 : 9780262161480
Total Pages : 312 pages
Book Rating : 4.1/5 (614 download)
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.
Author : Amir Shpilka
Publisher : Now Publishers Inc
ISBN 13 : 1601984006
Total Pages : 193 pages
Book Rating : 4.6/5 (19 download)
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.
Author : Hector Zenil
Publisher : World Scientific
ISBN 13 : 9814462632
Total Pages : 439 pages
Book Rating : 4.8/5 (144 download)
Download or read book Randomness Through Computation: Some Answers, More Questions written by Hector Zenil and published by World Scientific. This book was released on 2011-02-11 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This review volume consists of a set of chapters written by leading scholars, most of them founders of their fields. It explores the connections of Randomness to other areas of scientific knowledge, especially its fruitful relationship to Computability and Complexity Theory, and also to areas such as Probability, Statistics, Information Theory, Biology, Physics, Quantum Mechanics, Learning Theory and Artificial Intelligence. The contributors cover these topics without neglecting important philosophical dimensions, sometimes going beyond the purely technical to formulate age old questions relating to matters such as determinism and free will.The scope of Randomness Through Computation is novel. Each contributor shares their personal views and anecdotes on the various reasons and motivations which led them to the study of Randomness. Using a question and answer format, they share their visions from their several distinctive vantage points.
Author : Ingo Wegener
Publisher :
ISBN 13 :
Total Pages : 502 pages
Book Rating : 4.F/5 ( download)
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:
Author : Stasys Jukna
Publisher : Springer Science & Business Media
ISBN 13 : 3642245080
Total Pages : 618 pages
Book Rating : 4.6/5 (422 download)
Download or read book Boolean Function Complexity written by Stasys Jukna and published by Springer Science & Business Media. This book was released on 2012-01-06 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boolean circuit complexity is the combinatorics of computer science and involves many intriguing problems that are easy to state and explain, even for the layman. This book is a comprehensive description of basic lower bound arguments, covering many of the gems of this “complexity Waterloo” that have been discovered over the past several decades, right up to results from the last year or two. Many open problems, marked as Research Problems, are mentioned along the way. The problems are mainly of combinatorial flavor but their solutions could have great consequences in circuit complexity and computer science. The book will be of interest to graduate students and researchers in the fields of computer science and discrete mathematics.
Author : Howard Straubing
Publisher : Springer Science & Business Media
ISBN 13 : 1461202892
Total Pages : 235 pages
Book Rating : 4.4/5 (612 download)
Download or read book Finite Automata, Formal Logic, and Circuit Complexity written by Howard Straubing and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the connections between mathematical automata and for mal logic is as old as theoretical computer science itself. In the founding paper of the subject, published in 1936, Turing showed how to describe the behavior of a universal computing machine with a formula of first order predicate logic, and thereby concluded that there is no algorithm for deciding the validity of sentences in this logic. Research on the log ical aspects of the theory of finite-state automata, which is the subject of this book, began in the early 1960's with the work of J. Richard Biichi on monadic second-order logic. Biichi's investigations were extended in several directions. One of these, explored by McNaughton and Papert in their 1971 monograph Counter-free Automata, was the characterization of automata that admit first-order behavioral descriptions, in terms of the semigroup theoretic approach to automata that had recently been developed in the work of Krohn and Rhodes and of Schiitzenberger. In the more than twenty years that have passed since the appearance of McNaughton and Papert's book, the underlying semigroup theory has grown enor mously, permitting a considerable extension of their results. During the same period, however, fundamental investigations in the theory of finite automata by and large fell out of fashion in the theoretical com puter science community, which moved to other concerns.
Author : Bruce M. Kapron
Publisher : Morgan & Claypool
ISBN 13 :
Total Pages : 424 pages
Book Rating : 4.4/5 (7 download)
Download or read book Logic, Automata, and Computational Complexity written by Bruce M. Kapron and published by Morgan & Claypool. This book was released on 2023-05-22 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professor Stephen A. Cook is a pioneer of the theory of computational complexity. His work on NP-completeness and the P vs. NP problem remains a central focus of this field. Cook won the 1982 Turing Award for “his advancement of our understanding of the complexity of computation in a significant and profound way.” This volume includes a selection of seminal papers embodying the work that led to this award, exemplifying Cook’s synthesis of ideas and techniques from logic and the theory of computation including NP-completeness, proof complexity, bounded arithmetic, and parallel and space-bounded computation. These papers are accompanied by contributed articles by leading researchers in these areas, which convey to a general reader the importance of Cook’s ideas and their enduring impact on the research community. The book also contains biographical material, Cook’s Turing Award lecture, and an interview. Together these provide a portrait of Cook as a recognized leader and innovator in mathematics and computer science, as well as a gentle mentor and colleague.
Author : Stasys Jukna
Publisher : Springer Nature
ISBN 13 : 3031423542
Total Pages : 138 pages
Book Rating : 4.0/5 (314 download)
Download or read book Tropical Circuit Complexity written by Stasys Jukna and published by Springer Nature. This book was released on 2023-12-08 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an enticing introduction to tropical circuits and their use as a rigorous mathematical model for dynamic programming (DP), which is one of the most fundamental algorithmic paradigms for solving combinatorial, discrete optimization problems. In DP, an optimization problem is broken up into smaller subproblems that are solved recursively. Many classical DP algorithms are pure in that they only use the basic (min,+) or (max,+) operations in their recursion equations. In tropical circuits, these operations are used as gates. Thanks to the rigorous combinatorial nature of tropical circuits, elements from the Boolean and arithmetic circuit complexity can be used to obtain lower bounds for tropical circuits, which play a crucial role in understanding the limitations and capabilities of these computational models. This book aims to offer a toolbox for proving lower bounds on the size of tropical circuits. In this work, the reader will find lower-bound ideas and methods that have emerged in the last few years, with detailed proofs. Largely self-contained, this book is meant to be approachable by graduate students in mathematics and computer science with a special interest in circuit complexity.
Author : Kenneth Donald Hoover III
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (134 download)
Download or read book Connections Between and Techniques For Circuit Meta-Complexity Problems and Lower Bounds written by Kenneth Donald Hoover III and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation presents some circuit complexity results and techniques. Circuit complexity is a branch of computational complexity dealing with classes of circuit families as opposed to classes of Turing Machines. Recent research has shown that there are rich connections between circuit complexity and other areas in theoretical computer science: Carmosino et al. construct learning algorithms from "natural" circuit lower bounds; Murray and Williams show that slightly better than brute-force SAT algorithms lead to circuit lower bounds against NP, and; Ilango, Ren, and Santhanam show that the existence of one-way functions is equivalent to hard distributions with certain properties existing for the Minimum Circuit Size Problem (MCSP). A common theme throughout these results is the concept of "meta-algorithms," algorithms which take functions as input and attempt to either construct objects computing the function in some way (e.g. construct a circuit that well-approximates the function), or finding some computationally relevant quantity (e.g. what is the minimum size of a circuit computing the function). This dissertation will focus on circuit complexity and MCSP for classes of low-depth circuits, particularly those of bounded fan-in. Here, we will present a lifting theorem from small-constant-depth bounded bottom fan-in circuits to larger-constant-depth bounded bottom fan-in circuits, leading to a reduction between MCSP for the corresponding classes. As part of this, we also present a new switching lemma, which may be of independent interest. We then demonstrate that MCSP for depth-2 bounded bottom fan-in circuits is NP-hard to compute, and is approximable within a factor of O(log N). After, we give a barrier result stating that "natural" reductions between MCSP for different fixed-depth circuit classes yields unexpectedly fast MCSP algorithms or new circuit lower bounds against these classes. Finally, we introduce a family of new models of communication complexity and give some upper and lower bounds in these models, with an eye to separating P from fan-in 2 O(log n)-depth circuits.
Author : Manindra Agrawal
Publisher : Springer
ISBN 13 : 3319054465
Total Pages : 206 pages
Book Rating : 4.3/5 (19 download)
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.
Author : Mohammed Taghi Hajiaghayi
Publisher : Springer
ISBN 13 : 3319286781
Total Pages : 192 pages
Book Rating : 4.3/5 (192 download)
Download or read book Topics in Theoretical Computer Science written by Mohammed Taghi Hajiaghayi and published by Springer. This book was released on 2016-01-08 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the First IFIP WG 1.8 International Conference on Topics in Theoretical Computer Science, held in Tehran, Iran, in August 2015. The 10 full papers presented together with 3 invited talks were carefully reviewed and selected from 48 submissions. The papers feature novel and high-quality research in all areas of theoretical computer science.
Author : Ding-Zhu Du
Publisher : John Wiley & Sons
ISBN 13 : 1118031164
Total Pages : 511 pages
Book Rating : 4.1/5 (18 download)
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.
Author : Jin-yi Cai
Publisher : American Mathematical Soc.
ISBN 13 : 9780821885758
Total Pages : 234 pages
Book Rating : 4.8/5 (857 download)
Download or read book Advances in Computational Complexity Theory written by Jin-yi Cai and published by American Mathematical Soc.. This book was released on 1993-01-01 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Recent papers on computational complexity theory * Contributions by some of the leading experts in the field This book will prove to be of lasting value in this fast-moving field as it provides expositions not found elsewhere. The book touches on some of the major topics in complexity theory and thus sheds light on this burgeoning area of research.
Author : Ilias Kotsireas
Publisher : Springer Nature
ISBN 13 : 3030340295
Total Pages : 564 pages
Book Rating : 4.0/5 (33 download)
Download or read book Analysis of Experimental Algorithms written by Ilias Kotsireas and published by Springer Nature. This book was released on 2019-11-14 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed post-conference proceedings of the Special Event on the Analysis of Experimental Algorithms, SEA2 2019, held in Kalamata, Greece, in June 2019. The 35 revised full papers presented were carefully reviewed and selected from 45 submissions. The papers cover a wide range of topics in both computer science and operations research/mathematical programming. They focus on the role of experimentation and engineering techniques in the design and evaluation of algorithms, data structures, and computational optimization methods.
