Read Books Online and Download eBooks, EPub, PDF, Mobi, Kindle, Text Full Free.
An Improved Complexity Hierarchy On The Boolean Network Complexity And Formula Size Of Boolean Functions
Download An Improved Complexity Hierarchy On The Boolean Network Complexity And Formula Size Of Boolean Functions full books in PDF, epub, and Kindle. Read online An Improved Complexity Hierarchy On The Boolean Network Complexity And Formula Size Of Boolean Functions ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis An improved complexity hierarchy on the Boolean network complexity and formula size of Boolean functions by : Ingo Wegener
Download or read book An improved complexity hierarchy on the Boolean network complexity and formula size of Boolean functions written by Ingo Wegener and published by . This book was released on 1984 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Boolean Function Complexity by : Stasys Jukna
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.
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 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 The Complexity of Boolean Networks by : Paul E. Dunne
Download or read book The Complexity of Boolean Networks written by Paul E. Dunne and published by . This book was released on 1988 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Boolean Function Complexity by : Michael S. Paterson
Download or read book Boolean Function Complexity written by Michael S. Paterson and published by Cambridge University Press. This book was released on 1992-11-05 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here Professor Paterson brings together papers from the 1990 Durham symposium on Boolean function complexity. The participants include many well known figures in the field.
Book Synopsis Probabilistic Boolean Networks by : Ilya Shmulevich
Download or read book Probabilistic Boolean Networks written by Ilya Shmulevich and published by SIAM. This book was released on 2010-01-21 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive treatment of probabilistic Boolean networks, unifying different strands of current research and addressing emerging issues.
Book Synopsis An Introduction to Boolean Function Complexity by : Michael S. Paterson
Download or read book An Introduction to Boolean Function Complexity written by Michael S. Paterson and published by . This book was released on 1976 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: The complexity of a finite Boolean function may be defined with respect to its computation by networks of logical elements in a variety of ways. The three complexities of circuit size, formula size and depth are considered, and some of the principal results concerning their relationships and estimations are presented, with outlined proofs for some of ths simpler theorems. This survey is restricted to networks in which all two-argument logical functions may be used.
Book Synopsis Further Improvements in the Boolean Domain by : Bernd Steinbach
Download or read book Further Improvements in the Boolean Domain written by Bernd Steinbach and published by Cambridge Scholars Publishing. This book was released on 2019-01-18 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: The amount of digital systems supporting our daily life is increasing continuously. Improved technical facilities for their production have led to growing challenges for engineers and scientists working in the Boolean domain. A Boolean variable can only carry two different Boolean values: FALSE or TRUE (0 or 1), and has the best interference resistance in technical systems. However, a Boolean function exponentially depends on the number of its variables. This exponential complexity is the reason for major problems in the process of design and realization of circuits. According to Moore’s Law, the complexity of digital systems approximately doubles every 18 months. This requires comprehensive knowledge and techniques to solve very complex Boolean problems. This volume represents the third book in a series that provides further insights into the Boolean domain. Part 1 explores powerful models, methods and techniques which improve the efficiency in solving Boolean problems of extreme complexity. The universality of Boolean equations as a model to solve Non-deterministic Polynomial-time (NP) hard problems, as well as special properties of index generation functions, spectral techniques, or relational approaches, is discussed here. Both hardware devices, such as Field Programmable Gate Arrays (FPGAs) or Graphics Processing Units (GPUs), and optimized algorithms realized in software contribute to the acceleration of Boolean calculations. Part 2 contributes to the synthesis and visualization of digital circuits, and provides interesting new solutions for several types of circuits. A comprehensive collection of benchmarks supports the evolution of both existing and new synthesis approaches. The continuous reduction of the size of the transistors increases the challenges with regard to the reliability of the circuits. Part 3 describes several new approaches for the synthesis of reversible circuits. These approaches, as well as a classification of reversible functions, extend the basis of future quantum computers.
Book Synopsis The Computational Complexity of Equivalence and Isomorphism Problems by : Thomas Thierauf
Download or read book The Computational Complexity of Equivalence and Isomorphism Problems written by Thomas Thierauf and published by Springer Science & Business Media. This book was released on 2000-08-04 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: A computational model is a framework for doing computations according to certain specified rules on some input data. These models come for example from automata theory, formal language theory, logic, or circuit theory. The computational power of such a model can be judged by evaluating certain problems with respect to that model. The theory of computations is the study of the inherent difficulty of computational problems, that is, their computational complexity. This monograph analyzes the computational complexity of the satisfiability, equivalence, and almost-equivalence problems with respect to various computational models. In particular, Boolean formulas, circuits, and various kinds of branching programs are considered.
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 Lower Bounds for the Complexity of Restrictions of Boolean Functions by : A.V. Chashkin
Download or read book Lower Bounds for the Complexity of Restrictions of Boolean Functions written by A.V. Chashkin and published by . This book was released on 2018 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: The complexity of restrictions of Boolean functions is studied in various computational models. Lower bounds for the complexity of the most complicated restrictions to domains of fixed size are established. The complexity bounds are shown to be tight up to a constant multiplicative factor in the case of logic circuits. For every Boolean function of variables whose circuit size is greater than , where is an arbitrary positive constant, it is proved that there exists a domain in {0, 1} the restriction to which has a nonlinear circuit size that differs by a constant factor from the circuit size of the most complicated partial Boolean function defined on this domain. Any Boolean function of variables is proved to be uniquely determined by its values in no more than domains whose sizes are bounded from above by the product of the function complexity and.
Book Synopsis Branching Programs and Binary Decision Diagrams by : Ingo Wegener
Download or read book Branching Programs and Binary Decision Diagrams written by Ingo Wegener and published by SIAM. This book was released on 2000-01-01 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite functions (in particular, Boolean functions) play a fundamental role in computer science and discrete mathematics. This book describes representations of Boolean functions that have small size for many important functions and which allow efficient work with the represented functions. The representation size of important and selected functions is estimated, upper and lower bound techniques are studied, efficient algorithms for operations on these representations are presented, and the limits of those techniques are considered. This book is the first comprehensive description of theory and applications. Research areas like complexity theory, efficient algorithms, data structures, and discrete mathematics will benefit from the theory described in this book. The results described within have applications in verification, computer-aided design, model checking, and discrete mathematics. This is the only book to investigate the representation size of Boolean functions and efficient algorithms on these representations.
Book Synopsis Analysis and Control of Boolean Networks by : Daizhan Cheng
Download or read book Analysis and Control of Boolean Networks written by Daizhan Cheng and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis and Control of Boolean Networks presents a systematic new approach to the investigation of Boolean control networks. The fundamental tool in this approach is a novel matrix product called the semi-tensor product (STP). Using the STP, a logical function can be expressed as a conventional discrete-time linear system. In the light of this linear expression, certain major issues concerning Boolean network topology – fixed points, cycles, transient times and basins of attractors – can be easily revealed by a set of formulae. This framework renders the state-space approach to dynamic control systems applicable to Boolean control networks. The bilinear-systemic representation of a Boolean control network makes it possible to investigate basic control problems including controllability, observability, stabilization, disturbance decoupling etc.
Book Synopsis Complexity Measures of Boolean Functions and Their Applications by : Siddhesh Prashant Chaubal
Download or read book Complexity Measures of Boolean Functions and Their Applications written by Siddhesh Prashant Chaubal and published by . This book was released on 2020 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central focus of computational complexity theory is to measure the "hardness" of computing different functions. Towards this end, several measures of complexity for Boolean functions have been studied over the past few decades. Examples of important complexity measures include sensitivity, block sensitivity, certificate complexity, decision tree complexity and degree. Studying the relationships between these different measures has been an active area of research. In the first part of this dissertation, we prove several results towards tightening the relationships between some of these measures - particularly, the sensitivity and block sensitivity. Specifically, we prove better (cubic and sometimes quadratic) upper bounds on block sensitivity in terms of sensitivity for certain classes of transitive functions. We also prove tight lower bounds on the block sensitivity for the classes we consider. In the other direction, we give various new constructions of families of Boolean functions that exhibit quadratic separation between sensitivity and block sensitivity. Our constructions have several novel aspects. For example, we give the first direct constructions of families of Boolean functions that have both 0-block sensitivity and 1-block sensitivity quadratically larger than sensitivity. In the next part of this dissertation, we introduce a new complexity measure of Boolean functions we call diameter, that captures the relationship between certificate complexity and several other measures of Boolean functions. We argue that estimating diameter may help to get improved bounds on certificate complexity in terms of sensitivity, and other measures. Further, we prove tight bounds on the sensitivity and block sensitivity of transitive functions with constant diameter. We also prove some implications for the log-rank conjecture in communication complexity for XOR functions with bounded diameter. In the last part of this dissertation, we study applications of the relationship between some of these measures to machine learning. Specifically we contribute towards two problems concerning decision trees as a machine learning model. First, we focus on the problem of modifying a given decision tree classifier to optimize a specific evaluation measure (the recall of the classifier) under some constraints. Finally, we present some algorithms for decision trees for regression problems in the context of transfer learning
Book Synopsis A 2.75n-lower bound on the network complexity of Boolean functions by : Norbert Blum
Download or read book A 2.75n-lower bound on the network complexity of Boolean functions written by Norbert Blum and published by . This book was released on 1981 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Logical Foundations of Proof Complexity by : Stephen Cook
Download or read book Logical Foundations of Proof Complexity written by Stephen Cook and published by Cambridge University Press. This book was released on 2010-01-25 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. The result is a uniform treatment of many systems in the literature.
