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The Complexity Of The Optimal Variable Ordering Problems Of Shared Binary Decision Diagrams
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Book Synopsis The Complexity of the Optimal Variable Ordering Problems of Shared Binary Decision Diagrams by : Kyōto Daigaku. Joho Kogaku Kyoshitsu
Download or read book The Complexity of the Optimal Variable Ordering Problems of Shared Binary Decision Diagrams written by Kyōto Daigaku. Joho Kogaku Kyoshitsu and published by . This book was released on 1993 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "A binary decision diagram (BDD) proposed by Akers and Bryant is a directed acyclic graph for representing a Boolean function. BDD's are widely used in various areas which require Boolean function manipulation, since BDD's can represent efficiently many of Boolean functions for practical use and can have other desirable properties. A shared binary decision diagram (SBDD) is the extension of BDD's and represents more than one Boolean functions [sic]. Recently some improvements such as the introduction of attributed edges were proposed and SBDD's are used in wide areas such as logic design verification, test generation and logic synthesis. It is important to represent Boolean functions by the smaller size of BDD's or SBDD's, because computation time and storage requirements for Boolean function manipulation are highly influenced by the size of the graph. In general the number of nodes largely depends on the variable ordering. Therefore it is important to find a variable ordering that minimizes the size of the graph. From the theoretical point of view, it was shown by Bryant that the problem of computing a variable ordering that minimizes the size of the graph for a given Boolean formula is co NP-complete. However it has not been shown how hard it is to solve the problem of finding an optimal variable ordering for a given BDD. There is the case that the number of nodes of BDD's (an SBDD) corresponding to the Boolean formulas of the polynomial size is exponential for any variable ordering (for example, multiplier functions). Thus, since it is impossible to show a trivial polynomial transformation from the problem for a given Boolean formula to the problem for a given BDD, the two problems are essentially different. In this report, it is proved that the optimal variable ordering problem of SBDD (OVO) is NP- complete. The problem is to decide whether, for a given SBDD with n nodes and a positive integer k(
Book Synopsis The Complexity of the Optimal Variable Ordering Problems of a Shared Binary Decision Diagram by : Tōkyō Daigaku. Dept. of Information Science
Download or read book The Complexity of the Optimal Variable Ordering Problems of a Shared Binary Decision Diagram written by Tōkyō Daigaku. Dept. of Information Science and published by . This book was released on 1993 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "A binary decision diagram (BDD) is a directed acyclic graph for representing a Boolean function. BDD's are widely used in various areas which require Boolean function manipulation, since BDD's can represent efficiently many of practical Boolean functions and have other desirable properties. However the complexity of constructing BDD's has hardly been researched theoretically. In this report, we prove that the optimal variable ordering problem of a shared BDD is NP-complete, and touch on the approximation hardness of this problem and related problems of BDD's."
Book Synopsis The Complexity of the Optimal Variable Ordering Problems of Shard Binary Decision Diagrams by : S. Tani
Download or read book The Complexity of the Optimal Variable Ordering Problems of Shard Binary Decision Diagrams written by S. Tani and published by . This book was released on 1993 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book STACS 98 written by Michel Morvan and published by Springer Science & Business Media. This book was released on 1998-02-18 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the strictly refereed proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science, STACS 98, held in Paris, France, in February 1998. The volume presents three invited surveys together with 52 revised full papers selected from a total of 155 submissions. The papers are organized in topical sections on algorithms and data structures, logic, complexity, and automata and formal languages.
Book Synopsis Handbook of Model Checking by : Edmund M. Clarke
Download or read book Handbook of Model Checking written by Edmund M. Clarke and published by Springer. This book was released on 2018-05-18 with total page 1210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model checking is a computer-assisted method for the analysis of dynamical systems that can be modeled by state-transition systems. Drawing from research traditions in mathematical logic, programming languages, hardware design, and theoretical computer science, model checking is now widely used for the verification of hardware and software in industry. The editors and authors of this handbook are among the world's leading researchers in this domain, and the 32 contributed chapters present a thorough view of the origin, theory, and application of model checking. In particular, the editors classify the advances in this domain and the chapters of the handbook in terms of two recurrent themes that have driven much of the research agenda: the algorithmic challenge, that is, designing model-checking algorithms that scale to real-life problems; and the modeling challenge, that is, extending the formalism beyond Kripke structures and temporal logic. The book will be valuable for researchers and graduate students engaged with the development of formal methods and verification tools.
Book Synopsis Computing and Combinatorics by : Tao Jiang
Download or read book Computing and Combinatorics written by Tao Jiang and published by Springer Science & Business Media. This book was released on 1997-07-30 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is aimed at graduate students, researchers, engineers and physicists involved in fluid computations. An up-to-date account is given of the present state of the art of numerical methods employed in computational fluid dynamics. The underlying numerical principles are treated with a fair amount of detail, using elementary methods. Attention is given to the difficulties arising from geometric complexity of the flow domain. Uniform accuracy for singular perturbation problems is studied, pointing the way to accurate computation of flows at high Reynolds number. Unified methods for compressible and incompressible flows are discussed. A treatment of the shallow-water equations is included. A basic introduction is given to efficient iterative solution methods. Many pointers are given to the current literature, facilitating further study.
Book Synopsis Algorithms and Computation by : Kam W. Ng
Download or read book Algorithms and Computation written by Kam W. Ng and published by Springer Science & Business Media. This book was released on 1993-11-26 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the fourth annual International Symposium on Algorithms and Computation, held in Hong Kong in December 1993.Numerous selected papers present original research in such areas as design and analysis of algorithms, computational complexity, and theory of computation. Topics covered include: - automata, languages, and computability, - combinatorial, graph, geometric, and randomized algorithms, - networks and distributed algorithms, - VLSIand parallel algorithms, - theory of learning and robotics, - number theory and robotics. Three invited papers are also included.
Book Synopsis Representations of Discrete Functions by : Tsutomu Sasao
Download or read book Representations of Discrete Functions written by Tsutomu Sasao and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Representations of Discrete Functions is an edited volume containing 13 chapter contributions from leading researchers with a focus on the latest research results. The first three chapters are introductions and contain many illustrations to clarify concepts presented in the text. It is recommended that these chapters are read first. The book then deals with the following topics: binary decision diagrams (BDDs), multi-terminal binary decision diagrams (MTBDDs), edge-valued binary decision diagrams (EVBDDs), functional decision diagrams (FDDs), Kronecker decision diagrams (KDDs), binary moment diagrams (BMDs), spectral transform decision diagrams (STDDs), ternary decision diagrams (TDDs), spectral transformation of logic functions, other transformations oflogic functions, EXOR-based two-level expressions, FPRM minimization with TDDs and MTBDDs, complexity theories on FDDs, multi-level logic synthesis, and complexity of three-level logic networks. Representations of Discrete Functions is designed for CAD researchers and engineers and will also be of interest to computer scientists who are interested in combinatorial problems. Exercises prepared by the editors help make this book useful as a graduate level textbook.
Book Synopsis SOFSEM 2009: Theory and Practice of Computer Science by : Mogens Nielsen
Download or read book SOFSEM 2009: Theory and Practice of Computer Science written by Mogens Nielsen and published by Springer Science & Business Media. This book was released on 2009-01-12 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2009, held in Špindleruv Mlýn, Czech Republic, in January 2009. The 49 revised full papers, presented together with 9 invited contributions, were carefully reviewed and selected from 132 submissions. SOFSEM 2009 was organized around the following four tracks: Foundations of Computer Science; Theory and Practice of Software Services; Game Theoretic Aspects of E-commerce; and Techniques and Tools for Formal Verification.
Book Synopsis SOFSEM '98: Theory and Practice of Informatics by : Branislav Rovan
Download or read book SOFSEM '98: Theory and Practice of Informatics written by Branislav Rovan and published by Springer. This book was released on 2003-06-29 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 25th Seminar on Current Trends in Theory and Practice of Informatics, SOFSEM'98, held in Jasna, Slovakia, in November 1998. The volume presents 19 invited survey articles by internationally well-known authorities together with 18 revised full research papers carefully reviewed and selected for inclusion in the book. The areas covered include history of models of computation, algorithms, formal methods, practical aspects of software engineering, database systems, parallel and distributed systems, electronic commerce, and electronic documents and digital libraries.
Book Synopsis Decision Diagrams for Optimization by : David Bergman
Download or read book Decision Diagrams for Optimization written by David Bergman and published by Springer. This book was released on 2016-11-01 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a novel approach to discrete optimization, providing both theoretical insights and algorithmic developments that lead to improvements over state-of-the-art technology. The authors present chapters on the use of decision diagrams for combinatorial optimization and constraint programming, with attention to general-purpose solution methods as well as problem-specific techniques. The book will be useful for researchers and practitioners in discrete optimization and constraint programming. "Decision Diagrams for Optimization is one of the most exciting developments emerging from constraint programming in recent years. This book is a compelling summary of existing results in this space and a must-read for optimizers around the world." [Pascal Van Hentenryck]
Book Synopsis Mathematical Foundations of Computer Science 1994 by : Igor Privara
Download or read book Mathematical Foundations of Computer Science 1994 written by Igor Privara and published by Springer Science & Business Media. This book was released on 1994-08-03 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the proceedings of the 19th International Symposium on Mathematical Foundations of Theoretical Computer Science, MFCS '94, held in Kosice, Slovakia in August 1994. MFCS '94 brought together specialists in theoretical fields of computer science from various countries in order to stimulate mathematical research in theoretical computer science. Besides 12 papers based on invited talks by renowned experts, the book contains 42 research contributions selected from a total of 112 submissions. All areas of theoretical computer science are presented, some from a particular mathematical point of view.
Book Synopsis Experimental Algorithmics by : Rudolf Fleischer
Download or read book Experimental Algorithmics written by Rudolf Fleischer and published by Springer. This book was released on 2003-07-01 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Experimental algorithmics, as its name indicates, combines algorithmic work and experimentation: algorithms are not just designed, but also implemented and tested on a variety of instances. Perhaps the most important lesson in this process is that designing an algorithm is but the first step in the process of developing robust and efficient software for applications. Based on a seminar held at Dagstuhl Castle, Germany in September 2000, this state-of-the-art survey presents a coherent survey of the work done in the area so far. The 11 carefully reviewed chapters provide complete coverage of all current topics in experimental algorithmics.
Book Synopsis VLSI Circuits and Embedded Systems by : Hafiz Md. Hasan Babu
Download or read book VLSI Circuits and Embedded Systems written by Hafiz Md. Hasan Babu and published by CRC Press. This book was released on 2022-07-29 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very Large-Scale Integration (VLSI) creates an integrated circuit (IC) by combining thousands of transistors into a single chip. While designing a circuit, reduction of power consumption is a great challenge. VLSI designs reduce the size of circuits which eventually reduces the power consumption of the devices. However, it increases the complexity of the digital system. Therefore, computer-aided design tools are introduced into hardware design processes. Unlike the general-purpose computer, an embedded system is engineered to manage a wide range of processing tasks. Single or multiple processing cores manage embedded systems in the form of microcontrollers, digital signal processors, field-programmable gate arrays, and application-specific integrated circuits. Security threats have become a significant issue since most embedded systems lack security even more than personal computers. Many embedded systems hacking tools are readily available on the internet. Hacking in the PDAs and modems is a pervasive example of embedded systems hacking. This book explores the designs of VLSI circuits and embedded systems. These two vast topics are divided into four parts. In the book's first part, the Decision Diagrams (DD) have been covered. DDs have extensively used Computer-Aided Design (CAD) software to synthesize circuits and formal verification. The book's second part mainly covers the design architectures of Multiple-Valued Logic (MVL) Circuits. MVL circuits offer several potential opportunities to improve present VLSI circuit designs. The book's third part deals with Programmable Logic Devices (PLD). PLDs can be programmed to incorporate a complex logic function within a single IC for VLSI circuits and Embedded Systems. The fourth part of the book concentrates on the design architectures of Complex Digital Circuits of Embedded Systems. As a whole, from this book, core researchers, academicians, and students will get the complete picture of VLSI Circuits and Embedded Systems and their applications.
Book Synopsis Symbolic Model Checking by : Kenneth L. McMillan
Download or read book Symbolic Model Checking written by Kenneth L. McMillan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Formal verification means having a mathematical model of a system, a language for specifying desired properties of the system in a concise, comprehensible and unambiguous way, and a method of proof to verify that the specified properties are satisfied. When the method of proof is carried out substantially by machine, we speak of automatic verification. Symbolic Model Checking deals with methods of automatic verification as applied to computer hardware. The practical motivation for study in this area is the high and increasing cost of correcting design errors in VLSI technologies. There is a growing demand for design methodologies that can yield correct designs on the first fabrication run. Moreover, design errors that are discovered before fabrication can also be quite costly, in terms of engineering effort required to correct the error, and the resulting impact on development schedules. Aside from pure cost considerations, there is also a need on the theoretical side to provide a sound mathematical basis for the design of computer systems, especially in areas that have received little theoretical attention.
Download or read book Logic Design written by Wai-Kai Chen and published by CRC Press. This book was released on 2003-03-19 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume drawn from the VLSI Handbook, the focus is on logic design and compound semiconductor digital integrated circuit technology. Expert discussions cover topics ranging from the basics of logic expressions and switching theory to sophisticated programmable logic devices and the design of GaAs MESFET and HEMT logic circuits. Logic Design
