Author: Heribert Vollmer
Publisher: Springer Science & Business Media
ISBN: 3662039273
Category : Computers
Languages : en
Pages : 277
Get Book Here
Book Description
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: 0521424267
Category : Computers
Languages : en
Pages : 609
Get Book Here
Book Description
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: 9780262161480
Category : Computers
Languages : en
Pages : 312
Get Book Here
Book Description
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: 1601984006
Category : Computers
Languages : en
Pages : 193
Get Book Here
Book Description
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: Stasys Jukna
Publisher: Springer Science & Business Media
ISBN: 3642245080
Category : Mathematics
Languages : en
Pages : 618
Get Book Here
Book Description
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: Daniel Pierre Bovet
Publisher: Prentice Hall PTR
ISBN:
Category : Computers
Languages : en
Pages : 304
Get Book Here
Book Description
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.
Author: Oded Goldreich
Publisher: Cambridge University Press
ISBN: 9780521884730
Category : Computers
Languages : en
Pages : 632
Get Book Here
Book Description
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.
Author: Christos H. Papadimitriou
Publisher: MacMillan Publishing Company
ISBN: 9780020153085
Category : Computational complexity
Languages : en
Pages : 523
Get Book Here
Book Description
The first unified introduction and reference for the field of computational complexity. Virtually non-existent only 25 years ago, computational complexity has expanded tremendously and now comprises a major part of the researh activity in theoretical science.
Author: Troy Lee
Publisher: Now Publishers Inc
ISBN: 1601982585
Category : Computers
Languages : en
Pages : 152
Get Book Here
Book Description
The communication complexity of a function f(x, y) measures the number of bits that two players, one who knows x and the other who knows y, must exchange to determine the value f(x, y). Communication complexity is a fundamental measure of complexity of functions. Lower bounds on this measure lead to lower bounds on many other measures of computational complexity. This monograph surveys lower bounds in the field of communication complexity. Our focus is on lower bounds that work by first representing the communication complexity measure in Euclidean space. That is to say, the first step in these lower bound techniques is to find a geometric complexity measure, such as rank or trace norm, that serves as a lower bound to the underlying communication complexity measure. Lower bounds on this geometric complexity measure are then found using algebraic and geometric tools.
Author: Thomas Kropf
Publisher: Springer Science & Business Media
ISBN: 9783540634751
Category : Computers
Languages : en
Pages : 388
Get Book Here
Book Description
This state-of-the-art monograph presents a coherent survey of a variety of methods and systems for formal hardware verification. It emphasizes the presentation of approaches that have matured into tools and systems usable for the actual verification of nontrivial circuits. All in all, the book is a representative and well-structured survey on the success and future potential of formal methods in proving the correctness of circuits. The various chapters describe the respective approaches supplying theoretical foundations as well as taking into account the application viewpoint. By applying all methods and systems presented to the same set of IFIP WG10.5 hardware verification examples, a valuable and fair analysis of the strenghts and weaknesses of the various approaches is given.
