Advancing Algebraic And Logical Approaches To Circuit Lower Bounds

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Arithmetic Circuits

Author : Amir Shpilka
Publisher : Now Publishers Inc
ISBN 13 : 1601984006
Total Pages : 193 pages
Book Rating : 4.6/5 (19 download)

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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.

Logic and Scientific Methods

Author : Maria Luisa Dalla Chiara
Publisher : Springer Science & Business Media
ISBN 13 : 9780792343837
Total Pages : 564 pages
Book Rating : 4.3/5 (438 download)

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Book Synopsis Logic and Scientific Methods by : Maria Luisa Dalla Chiara

Download or read book Logic and Scientific Methods written by Maria Luisa Dalla Chiara and published by Springer Science & Business Media. This book was released on 1996-12-31 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of two volumes comprising the papers submitted for publication by the invited participants to the Tenth International Congress of Logic, Methodology and Philosophy of Science, held in Florence, August 1995. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science. The invited lectures published in the two volumes demonstrate much of what goes on in the fields of the Congress and give the state of the art of current research. The two volumes cover the traditional subdisciplines of mathematical logic and philosophical logic, as well as their interfaces with computer science, linguistics and philosophy. Philosophy of science is broadly represented, too, including general issues of natural sciences, social sciences and humanities. The papers in Volume One are concerned with logic, mathematical logic, the philosophy of logic and mathematics, and computer science.

Computational Complexity

Author : Sanjeev Arora
Publisher : Cambridge University Press
ISBN 13 : 0521424267
Total Pages : 609 pages
Book Rating : 4.5/5 (214 download)

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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.

Introduction to Circuit Complexity

Author : Heribert Vollmer
Publisher : Springer Science & Business Media
ISBN 13 : 3662039273
Total Pages : 277 pages
Book Rating : 4.6/5 (62 download)

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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.

Boolean Functions and Computation Models

Author : Peter Clote
Publisher : Springer Science & Business Media
ISBN 13 : 3662049430
Total Pages : 612 pages
Book Rating : 4.6/5 (62 download)

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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.

Advanced Techniques in Logic Synthesis, Optimizations and Applications

Author : Kanupriya Gulati
Publisher : Springer Science & Business Media
ISBN 13 : 1441975187
Total Pages : 423 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Advanced Techniques in Logic Synthesis, Optimizations and Applications by : Kanupriya Gulati

Download or read book Advanced Techniques in Logic Synthesis, Optimizations and Applications written by Kanupriya Gulati and published by Springer Science & Business Media. This book was released on 2010-11-25 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers recent advances in the field of logic synthesis and design, including Boolean Matching, Logic Decomposition, Boolean satisfiability, Advanced Synthesis Techniques and Applications of Logic Design. All of these topics are valuable to CAD engineers working in Logic Design, Logic Optimization, and Verification. Engineers seeking opportunities for optimizing VLSI integrated circuits will find this book as an invaluable reference, since there is no existing book that covers this material in a systematic fashion.

Mathematics and Computation

Author : Avi Wigderson
Publisher : Princeton University Press
ISBN 13 : 0691189137
Total Pages : 434 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Mathematics and Computation by : Avi Wigderson

Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

The Complexity of Boolean Functions

Author : Ingo Wegener
Publisher :
ISBN 13 :
Total Pages : 502 pages
Book Rating : 4.F/5 ( download)

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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:

7th International Symposium on Advanced Research in Asynchronous Circuits and Systems (ASYNC 2001)

Author :
Publisher :
ISBN 13 : 9780769510347
Total Pages : 234 pages
Book Rating : 4.5/5 (13 download)

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Book Synopsis 7th International Symposium on Advanced Research in Asynchronous Circuits and Systems (ASYNC 2001) by :

Download or read book 7th International Symposium on Advanced Research in Asynchronous Circuits and Systems (ASYNC 2001) written by and published by . This book was released on 2001 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprises 20 papers selected for presentation at the Async 2001 conference in March 2001, as well as three invited presentations from industry researchers. Papers were divided into seven sessions: systems/arithmetic; experiments; synthesis and verification; handshaking; communication; architecture; and performance analysis and optimization. The invited talks are titled Asynchronous Design and the Pursuit of Low Power; Where Are the Async Millionaires?; and Testing Asynchronous Circuits: Help Is on the Way! Indexed by author but not by subject. c. Book News Inc.

Lower Bounds in Communication Complexity

Author : Troy Lee
Publisher : Now Publishers Inc
ISBN 13 : 1601982585
Total Pages : 152 pages
Book Rating : 4.6/5 (19 download)

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Book Synopsis Lower Bounds in Communication Complexity by : Troy Lee

Download or read book Lower Bounds in Communication Complexity written by Troy Lee and published by Now Publishers Inc. This book was released on 2009 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Advances in Computational Science and Engineering

Author : Laurence Tianruo Yang
Publisher : Springer
ISBN 13 : 3642102387
Total Pages : 269 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Advances in Computational Science and Engineering by : Laurence Tianruo Yang

Download or read book Advances in Computational Science and Engineering written by Laurence Tianruo Yang and published by Springer. This book was released on 2009-11-02 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: As communication and networking (CN) become specialized and fragmented, it is easy to lose sight that many topics in CN have common threads and because of this, advances in one sub-discipline may transmit to another. The presentation of results between different sub-disciplines of CN encourages this interchange for the advan- ment of CN as a whole. Of particular interest is the hybrid approach of combining ideas from one discipline with those of another to achieve a result that is more signi- cant than the sum of the individual parts. Through this hybrid philosophy, a new or common principle can be discovered which has the propensity to propagate throu- out this multifaceted discipline. This volume comprises the selection of extended versions of papers that were p- sented in their shortened form at the 2008 International Conference on Future Gene- tion Communication and Networking (http://www. sersc. org/FGCN2008/), Inter- tional Conference on Bio-Science and Bio-Technology (http://www. sersc. org/ BSBT2008/), International Symposium on u- and e- Service, Science and Technology (http://www. sersc. org/UNESST2008/), International Symposium on Database Theory and Application (http://www. sersc. org/DTA2008/), International Symposium on Control and Automation (http://www. sersc. org/CA2008/), International Symposium on Signal Processing, Image Processing and Pattern Recognition (http://www. sersc. org/SIP2008/), International Symposium on Grid and Distributed Computing (ttp://www. sersc. org/ GDC2008/), International Symposium on Smart Home (http://www. sersc. org/SH2008/), and 2009 Advanced Science and Technology (http://www. sersc. org/AST2009/).

Analysis of Boolean Functions

Author : Ryan O'Donnell
Publisher : Cambridge University Press
ISBN 13 : 1107038324
Total Pages : 445 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Analysis of Boolean Functions by : Ryan O'Donnell

Download or read book Analysis of Boolean Functions written by Ryan O'Donnell and published by Cambridge University Press. This book was released on 2014-06-05 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text gives a thorough overview of the analysis of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics.

Boolean Models and Methods in Mathematics, Computer Science, and Engineering

Author : Yves Crama
Publisher : Cambridge University Press
ISBN 13 : 0521847524
Total Pages : 781 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Boolean Models and Methods in Mathematics, Computer Science, and Engineering by : Yves Crama

Download or read book Boolean Models and Methods in Mathematics, Computer Science, and Engineering written by Yves Crama and published by Cambridge University Press. This book was released on 2010-06-28 with total page 781 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers written by prominent experts that examine a variety of advanced topics related to Boolean functions and expressions.

Design systems for VLSI circuits

Author : Giovanni DeMicheli
Publisher : Springer Science & Business Media
ISBN 13 : 9789024735624
Total Pages : 668 pages
Book Rating : 4.7/5 (356 download)

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Book Synopsis Design systems for VLSI circuits by : Giovanni DeMicheli

Download or read book Design systems for VLSI circuits written by Giovanni DeMicheli and published by Springer Science & Business Media. This book was released on 1987-07-31 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute, L'Aquila, Italy, July 7-18, 1986

Graduate Courses and Programs

Author : Iowa State University
Publisher :
ISBN 13 :
Total Pages : 366 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Graduate Courses and Programs by : Iowa State University

Download or read book Graduate Courses and Programs written by Iowa State University and published by . This book was released on 1997 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Molecular Electronics, Circuits, and Processing Platforms

Author : Sergey Edward Lyshevski
Publisher : CRC Press
ISBN 13 : 1351835203
Total Pages : 280 pages
Book Rating : 4.3/5 (518 download)

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Book Synopsis Molecular Electronics, Circuits, and Processing Platforms by : Sergey Edward Lyshevski

Download or read book Molecular Electronics, Circuits, and Processing Platforms written by Sergey Edward Lyshevski and published by CRC Press. This book was released on 2018-10-03 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: When microelectronic devices replaced vacuum tubes, it marked a revolution in electronics that opened the way to the computer age. We are on the verge of witnessing another equally profound shift. As molecular devices replace semiconductors, we will achieve new levels of performance, functionality and capability that will hugely impact electronics, as well as signal processing and computing. Molecular Electronics, Circuits, and Processing Platforms guides you confidently into this emerging field. Helping you to forge into the molecular frontier, this book examines the various concepts, methods and technologies used to approach and solve a wide variety of problems. The author works from new devices to systems and platforms. He also covers device-level physics, system-level design, analysis, and advanced fabrication technologies. Explore the latest and emerging molecular, biomolecular, and nanoscale processing platforms for building the next generation of circuits, memories and computations. By examining both solved and open issues, this book thoroughly develops the basic theory and shows you how to apply this knowledge toward new developments and practical hardware implementation. Don’t fall behind. Let Molecular Electronics, Circuits, and Processing Platforms take you to the next level of electronics design and applications.

Algebraic Complexity Theory

Author : Peter Bürgisser
Publisher : Springer Science & Business Media
ISBN 13 : 3662033380
Total Pages : 630 pages
Book Rating : 4.6/5 (62 download)

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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.