Connections Between And Techniques For Circuit Meta Complexity Problems And Lower Bounds

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Connections Between and Techniques For Circuit Meta-Complexity Problems and Lower Bounds

Author : Kenneth Donald Hoover III
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (134 download)

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Book Synopsis Connections Between and Techniques For Circuit Meta-Complexity Problems and Lower Bounds by : Kenneth Donald Hoover III

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.

Meta-algorithms Versus Circuit Lower Bounds

Author : Ruiwen Chen
Publisher :
ISBN 13 :
Total Pages : 150 pages
Book Rating : 4.:/5 (112 download)

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Book Synopsis Meta-algorithms Versus Circuit Lower Bounds by : Ruiwen Chen

Download or read book Meta-algorithms Versus Circuit Lower Bounds written by Ruiwen Chen and published by . This book was released on 2014 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational complexity theory and algorithms are two major areas in theoretical computer science. Computational complexity theorists study the inherent difficulty of computational problems, and classify problems based on computational resources needed. In particular, complexity theorists intend to prove lower bounds, that is, showing certain problems are not solvable under specific resource bounds. On the other hand, algorithm designers wish to discover efficient algorithms solving particular problems. Traditionally, researchers in the two areas have different goals and use different techniques. However, several recent breakthroughs indicate fundamental connections in between. In particular, new lower bounds were proved via designing efficient algorithms, and reversely, known lower bound proofs were exploited to design efficient algorithms. In this thesis, we focus on the connections between algorithms and lower bounds, which lead to discoveries of new algorithms and lower bounds. For small-size boolean formulas, we get new satisfiability counting algorithms. The algorithm is based on a simplified proof of the property that formula size shrinks with high probability under certain random restrictions. This approach is further adapted to get satisfiability algorithms and average-case lower bounds for small linear-size boolean circuits. We also show that circuit lower bound proofs based on the method of random restrictions yield non-trivial compression algorithms for easy boolean functions from the corresponding circuit classes. In the reverse, we show that the existence of non-trivial compression algorithms would imply circuit lower bounds for non-deterministic exponential time. In the end, we introduce the notion of weakly-uniform circuits, and generalize previous known lower bounds against uniform circuits to weakly-uniform circuits.

Connections Between Circuit Analysis Problems and Circuit Lower Bounds

Author : Cody Daniel Murray
Publisher :
ISBN 13 :
Total Pages : 112 pages
Book Rating : 4.:/5 (18 download)

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Book Synopsis Connections Between Circuit Analysis Problems and Circuit Lower Bounds by : Cody Daniel Murray

Download or read book Connections Between Circuit Analysis Problems and Circuit Lower Bounds written by Cody Daniel Murray and published by . This book was released on 2018 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: A circuit analysis problem takes a Boolean function f as input (where f is represented either as a logical circuit, or as a truth table) and determines some interesting property of f. Examples of circuit analysis problems include Circuit Satisfiability, Circuit Composition, and the Minimum Size Circuit Problem (MCSP). A circuit lower bound presents an interesting function f and shows that no "easy" family of logical circuits can compute f correctly on all inputs, for some definition of "easy". Lower bounds are infamously hard to prove, but are of significant interest for understanding computation. In this thesis, we derive new connections between circuit analysis problems and circuit lower bounds, to prove new lower bounds for various well-studied circuit classes. We show how faster algorithms for Circuit Satisfiability can imply non-uniform lower bounds for functions in NP and related classes. We prove that MCSP cannot be NP-hard under "local" gadget reductions of the kind that appear in textbooks, and if MCSP proved to be NP-hard in the usual (polynomial-time reduction) sense then we would also prove longstanding lower bounds in other regimes. We also prove that natural versions of the Circuit Composition problem do not have small circuits that are constructible in very small (logarithmic) space.

Computational Limitations of Small-depth Circuits

Author : Johan Håstad
Publisher : MIT Press (MA)
ISBN 13 :
Total Pages : 112 pages
Book Rating : 4.:/5 (41 download)

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Book Synopsis Computational Limitations of Small-depth Circuits by : Johan Håstad

Download or read book Computational Limitations of Small-depth Circuits written by Johan Håstad and published by MIT Press (MA). This book was released on 1987 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proving lower bounds on the amount of resources needed to compute specific functions is one of the most active branches of theoretical computer science. Significant progress has been made recently in proving lower bounds in two restricted models of Boolean circuits. One is the model of small depth circuits, and in this book Johan Torkel Hastad has developed very powerful techniques for proving exponential lower bounds on the size of small depth circuits' computing functions. The techniques described in Computational Limitations for Small Depth Circuitscan be used to demonstrate almost optimal lower bounds on the size of small depth circuits computing several different functions, such as parity and majority. The main tool used in the proof of the lower bounds is a lemma, stating that any AND of small fanout OR gates can be converted into an OR of small fanout AND gates with high probability when random values are substituted for the variables. Hastad also applies this tool to relativized complexity, and discusses in great detail the computation of parity and majority in small depth circuits. Contents:Introduction. Small Depth Circuits. Outline of Lower Bound Proofs. Main Lemma. Lower Bounds for Small Depth Circuits. Functions Requiring Depth k to Have Small Circuits. Applications to Relativized Complexity. How Well Can We Compute Parity in Small Depth? Is Majority Harder than Parity? Conclusions. John Hastad is a postdoctoral fellow in the Department of Mathematics at MIT Computational Limitations of Small Depth Circuitsis a winner of the 1986 ACM Doctoral Dissertation Award.

Advancing Algebraic and Logical Approaches to Circuit Lower Bounds

Author :
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (814 download)

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Book Synopsis Advancing Algebraic and Logical Approaches to Circuit Lower Bounds by :

Download or read book Advancing Algebraic and Logical Approaches to Circuit Lower Bounds written by and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complexity theory attempts to classify problems into classes according to their resource requirements such as time and space, and to understand the relative power of these resources. This dissertation is motivated, in particular, by the study of the limitations of Boolean and arithmetic circuits as models of computation. The goal of this area is to show that there are explicit problems that cannot be solved by small circuits. To this end we make progress along several avenues for proving such circuit lower bounds. Polynomial Identity Testing is the fundamental problem of testing whether a given multivariate polynomial is identically zero. There is a natural efficient randomized algorithm. Showing that there is an efficient deterministic identity test, in a sufficiently general setting, implies long elusive circuit lower bounds. In the first part of this dissertation, we develop new deterministic identity tests for bounded-read multilinear arithmetic formulas, an interesting class of polynomials that encompasses and significantly generalizes several prior works. Locality is a property of logical formulas that expresses that the formula cannot distinguish between two inputs that appear the same up to some distance parameter. Once established for a given set of logical formulas, the property can often be used to quickly argue separations from that set. In this dissertation we tightly characterize the locality of a logical system corresponding to AC0, the class of languages solvable by families of constant-depth polynomial-size Boolean circuits. In doing so we give a meta-theorem for proving that certain graph properties cannot be computed in AC0. Kernelization is the process of transforming an equivalent instance of one problem into an instance of another problem where the size of the latter instance depends only on a single parameter. We look at a set system that is motivated by the study of kernelization, and give a tight bound on the size of that set system.

Automata, Languages and Programming

Author : Luca Aceto
Publisher : Springer Science & Business Media
ISBN 13 : 3642220053
Total Pages : 825 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Automata, Languages and Programming by : Luca Aceto

Download or read book Automata, Languages and Programming written by Luca Aceto and published by Springer Science & Business Media. This book was released on 2011-06-27 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNCS 6755 and LNCS 6756 constitutes the refereed proceedings of the 38th International Colloquium on Automata, Languages and Programming, ICALP 2011, held in Zürich, Switzerland, in July 2011. The 114 revised full papers (68 papers for track A, 29 for track B, and 17 for track C) presented together with 4 invited talks, 3 best student papers, and 3 best papers were carefully reviewed and selected from a total of 398 submissions. The papers are grouped in three major tracks on algorithms, complexity and games; on logic, semantics, automata, and theory of programming; as well as on foundations of networked computation: models, algorithms and information management.

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.

Communication Complexity (for Algorithm Designers)

Author : Tim Roughgarden
Publisher : Foundations and Trends (R) in Theoretical Computer Science
ISBN 13 : 9781680831146
Total Pages : 206 pages
Book Rating : 4.8/5 (311 download)

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Book Synopsis Communication Complexity (for Algorithm Designers) by : Tim Roughgarden

Download or read book Communication Complexity (for Algorithm Designers) written by Tim Roughgarden and published by Foundations and Trends (R) in Theoretical Computer Science. This book was released on 2016-05-11 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals mostly with impossibility results - lower bounds on what can be accomplished by algorithms. However, the perspective is unapologetically that of an algorithm designer. The reader will learn lower bound technology on a "need-to-know" basis, guided by fundamental algorithmic problems that we care about.

Recent Awards in Engineering

Author :
Publisher :
ISBN 13 :
Total Pages : 986 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Recent Awards in Engineering by :

Download or read book Recent Awards in Engineering written by and published by . This book was released on 1983 with total page 986 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Proceedings of the ...ACM Symposium on Theory of Computing

Author :
Publisher :
ISBN 13 :
Total Pages : 752 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Proceedings of the ...ACM Symposium on Theory of Computing by :

Download or read book Proceedings of the ...ACM Symposium on Theory of Computing written by and published by . This book was released on 2003 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt:

VLSI Circuits for Biomedical Applications

Author : Krzysztof Iniewski
Publisher : Artech House
ISBN 13 : 1596933186
Total Pages : 453 pages
Book Rating : 4.5/5 (969 download)

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Book Synopsis VLSI Circuits for Biomedical Applications by : Krzysztof Iniewski

Download or read book VLSI Circuits for Biomedical Applications written by Krzysztof Iniewski and published by Artech House. This book was released on 2008 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Supported with over 280 illustrations and over 160 equations, the book offers cutting-edge guidance on designing integrated circuits for wireless biosensing, body implants, biosensing interfaces, and molecular biology. You discover innovative design techniques and novel materials to help you achieve higher levels circuit and system performance.

Miniaturization Technologies

Author :
Publisher : Office of Technology Assessment
ISBN 13 :
Total Pages : 64 pages
Book Rating : 4.3/5 (121 download)

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Book Synopsis Miniaturization Technologies by :

Download or read book Miniaturization Technologies written by and published by Office of Technology Assessment. This book was released on 1991 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

EDA for IC Implementation, Circuit Design, and Process Technology

Author : Luciano Lavagno
Publisher : CRC Press
ISBN 13 : 1420007955
Total Pages : 608 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis EDA for IC Implementation, Circuit Design, and Process Technology by : Luciano Lavagno

Download or read book EDA for IC Implementation, Circuit Design, and Process Technology written by Luciano Lavagno and published by CRC Press. This book was released on 2018-10-03 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting a comprehensive overview of the design automation algorithms, tools, and methodologies used to design integrated circuits, the Electronic Design Automation for Integrated Circuits Handbook is available in two volumes. The second volume, EDA for IC Implementation, Circuit Design, and Process Technology, thoroughly examines real-time logic to GDSII (a file format used to transfer data of semiconductor physical layout), analog/mixed signal design, physical verification, and technology CAD (TCAD). Chapters contributed by leading experts authoritatively discuss design for manufacturability at the nanoscale, power supply network design and analysis, design modeling, and much more. Save on the complete set.

Layout Minimization of CMOS Cells

Author : Robert L. Maziasz
Publisher : Springer Science & Business Media
ISBN 13 : 1461536243
Total Pages : 176 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Layout Minimization of CMOS Cells by : Robert L. Maziasz

Download or read book Layout Minimization of CMOS Cells written by Robert L. Maziasz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: The layout of an integrated circuit (lC) is the process of assigning geometric shape, size and position to the components (transistors and connections) used in its fabrication. Since the number of components in modem ICs is enormous, computer aided-design (CAD) programs are required to automate the difficult layout process. Prior CAD methods are inexact or limited in scope, and produce layouts whose area, and consequently manufacturing costs, are larger than necessary. This book addresses the problem of minimizing exactly the layout area of an important class of basic IC structures called CMOS cells. First, we precisely define the possible goals in area minimization for such cells, namely width and height minimization, with allowance for area-reducing reordering of transistors. We reformulate the layout problem in terms of a graph model and develop new graph-theoretic concepts that completely characterize the fundamental area minimization problems for series-parallel and nonseries-parallel circuits. These concepts lead to practical algorithms that solve all the basic layout minimization problems exactly, both for a single cell and for a one-dimensional array of such cells. Although a few of these layout problems have been solved or partially solved previously, we present here the first complete solutions to all the problems of interest.

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: 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

Crucial Issues in Semiconductor Materials and Processing Technologies

Author : S. Coffa
Publisher : Springer Science & Business Media
ISBN 13 : 940112714X
Total Pages : 523 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Crucial Issues in Semiconductor Materials and Processing Technologies by : S. Coffa

Download or read book Crucial Issues in Semiconductor Materials and Processing Technologies written by S. Coffa and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semiconductors lie at the heart of some of the most important industries and technologies of the twentieth century. The complexity of silicon integrated circuits is increasing considerably because of the continuous dimensional shrinkage to improve efficiency and functionality. This evolution in design rules poses real challenges for the materials scientists and processing engineers. Materials, defects and processing now have to be understood in their totality. World experts discuss, in this volume, the crucial issues facing lithography, ion implication and plasma processing, metallization and insulating layer quality, and crystal growth. Particular emphasis is placed upon silicon, but compound semiconductors and photonic materials are also highlighted. The fundamental concepts of phase stability, interfaces and defects play a key role in understanding these crucial issues. These concepts are reviewed in a crucial fashion.