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A Heuristic Approach To Variables Ordering In Binary Decision Diagram
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Book Synopsis Heuristics to Optimize the Variable Ordering in Binary Decision Diagrams by : Marvin Caspar
Download or read book Heuristics to Optimize the Variable Ordering in Binary Decision Diagrams written by Marvin Caspar and published by GRIN Verlag. This book was released on 2021-10-19 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seminar paper from the year 2019 in the subject Computer Science - Commercial Information Technology, grade: 1,0, University of Kaiserslautern, language: English, abstract: In this paper, two fault trees are examined, for which five heuristics are applied to evaluate and compare their effectiveness. The arrangement of variables in a Binary Decision Diagram (BDD) determines the size of the BDD after applying reduction rules and thus plays a decisive role in finding a compact representation of the Boolean function. Since there are already many possible arrangements with only a few variables and techniques for finding the optimal solution requiring too much time, the use of heuristics is needed. The main focus is on known approaches and especially on the dynamic method of the sifting algorithm.
Book Synopsis A Heuristic Approach to Variables Ordering in Binary Decision Diagram by : Jim-Eng Ng
Download or read book A Heuristic Approach to Variables Ordering in Binary Decision Diagram written by Jim-Eng Ng and published by . This book was released on 2000 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fault Tree is a well-known way of expressing failure combinations of a system. The Fault Tree analysis process, however, is computationally expensive and time consuming as the size of a Fault Tree increases. Binary Decision Diagram (BDD) is a Directed Acyclic Graph (DAG) encoding of a Fault Tree. This has been shown to be the most effective way of evaluating a Fault Tree. The encoding method employs an If-Then-Else (ite) methodology to represent the functionality of a system based on its events. The only drawback of BDD is that the size of the diagram is highly dependent on the ordering of the events that are used in the process of analysis. This paper inspects the relationship of the factors that affect the events ordering and present an ordering heuristic that will yield a reasonable size of BDD for all different formation of Fault Trees. Random trees are generated to experiment using simulation with a given number of events and gates. The BDD analysis results show that it reduces the overall sizes of a BDD for a given fault tree.
Book Synopsis Binary Decision Diagrams by : Rolf Drechsler
Download or read book Binary Decision Diagrams written by Rolf Drechsler and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: For someone with a hammer the whole world looks like a nail. Within the last 10-13 years Binar·y Decision Diagmms (BDDs) have become the state-of-the-art data structure in VLSI CAD for representation and ma nipulation of Boolean functions. Today, BDDs are widely used and in the meantime have also been integrated in commercial tools, especially in the area of verijication and synthesis. The interest in BDDs results from the fact that the data structure is generally accepted as providing a good compromise between conciseness of representation and efficiency of manipulation. With increasing number of applications, also in non CAD areas, classical methods to handle BDDs are being improved and new questions and problems evolve and have to be solved. The book should help the reader who is not familiar with BDDs (or DDs in general) to get a quick start. On the other hand it will discuss several new aspects of BDDs, e.g. with respect to minimization and implementation of a package. This will help people working with BDDs (in industry or academia) to keep informed about recent developments in this area.
Book Synopsis Binary Decision Diagrams and Applications for VLSI CAD by : Shin-ichi Minato
Download or read book Binary Decision Diagrams and Applications for VLSI CAD written by Shin-ichi Minato and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symbolic Boolean manipulation using binary decision diagrams (BDDs) has been successfully applied to a wide variety of tasks, particularly in very large scale integration (VLSI) computer-aided design (CAD). The concept of decision graphs as an abstract representation of Boolean functions dates back to the early work by Lee and Akers. In the last ten years, BDDs have found widespread use as a concrete data structure for symbolic Boolean manipulation. With BDDs, functions can be constructed, manipulated, and compared by simple and efficient graph algorithms. Since Boolean functions can represent not just digital circuit functions, but also such mathematical domains as sets and relations, a wide variety of CAD problems can be solved using BDDs. `Binary Decision Diagrams and Applications for VLSI CAD provides valuable information for both those who are new to BDDs as well as to long time aficionados.' -from the Foreword by Randal E. Bryant. `Over the past ten years ... BDDs have attracted the attention of many researchers because of their suitability for representing Boolean functions. They are now widely used in many practical VLSI CAD systems. ... this book can serve as an introduction to BDD techniques and ... it presents several new ideas on BDDs and their applications. ... many computer scientists and engineers will be interested in this book since Boolean function manipulation is a fundamental technique not only in digital system design but also in exploring various problems in computer science.' - from the Preface by Shin-ichi Minato.
Book Synopsis Variable Ordering Heuristics for Binary Decision Diagrams by : Lisa Marie Bartlett
Download or read book Variable Ordering Heuristics for Binary Decision Diagrams written by Lisa Marie Bartlett and published by . This book was released on 2000 with total page 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.
Book Synopsis How to Cope with an Intractable Problem by : Debajit Sensarma
Download or read book How to Cope with an Intractable Problem written by Debajit Sensarma and published by LAP Lambert Academic Publishing. This book was released on 2013 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two-level logic minimization is an attractive topic in the active research domain and it is a central problem in logic synthesis, as well as in reliability analysis and automated reasoning and other real life applications. But, this Two-level logic minimization problem involves computationally intractable problems and many heuristic approaches have been developed to cope with this problem. This book contains the work which deals with the Two-level logic minimization problem using a popular data structure called Binary Decision Diagram (BDD) which is an important family of data structures that have rapidly become the method of choice for representing and manipulating Boolean Functions inside a computer. Also the implicit set manipulation techniques based on BDD could be used with success to compute the sets of Prime and Essential Prime Implicants of Boolean Functions for which these sets are too large to be explicitly built. So, this feature of BDD, the proper variable ordering of the BDD, Reduced Ordered BDD and other heuristic methods are used in this work for solving the Two-level logic minimization problem for the functions which generates large set of Prime Implicants.
Book Synopsis A Binary Decision Diagram Approach for Finite State Machine Encoding by : Pi-Fuang Chen
Download or read book A Binary Decision Diagram Approach for Finite State Machine Encoding written by Pi-Fuang Chen and published by . This book was released on 1997 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 Advanced BDD Optimization by : Rudiger Ebendt
Download or read book Advanced BDD Optimization written by Rudiger Ebendt and published by Springer Science & Business Media. This book was released on 2005-12-05 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: VLSI CADhas greatly bene?ted from the use of reduced ordered Binary Decision Diagrams (BDDs) and the clausal representation as a problem of Boolean Satis?ability (SAT), e.g. in logic synthesis, ver- cation or design-for-testability. In recent practical applications, BDDs are optimized with respect to new objective functions for design space exploration. The latest trends show a growing number of proposals to fuse the concepts of BDD and SAT. This book gives a modern presentation of the established as well as of recent concepts. Latest results in BDD optimization are given, c- ering di?erent aspects of paths in BDDs and the use of e?cient lower bounds during optimization. The presented algorithms include Branch ? and Bound and the generic A -algorithm as e?cient techniques to - plore large search spaces. ? The A -algorithm originates from Arti?cial Intelligence (AI), and the EDA community has been unaware of this concept for a long time. Re- ? cently, the A -algorithm has been introduced as a new paradigm to explore design spaces in VLSI CAD. Besides AI search techniques, the book also discusses the relation to another ?eld of activity bordered to VLSI CAD and BDD optimization: the clausal representation as a SAT problem.
Book Synopsis Computational Intelligence. Theory and Applications by : Bernd Reusch
Download or read book Computational Intelligence. Theory and Applications written by Bernd Reusch and published by Springer. This book was released on 2003-06-30 with total page 1020 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ten years of ,,Fuzzy Days“ in Dortmund! What started as a relatively small workshop in 1991 has now become one of the best known smaller conferences on Computational Intelligence in the world. It fact, it was (to my best knowledge) the ?rst conference to use this term, in 1994, although I confess that another, larger conference was announced ?rst and the trade mark “Computational Intelligence was not coined in Dortmund. I believe, that the success of this conference is grounded on the quality of its reviewedandinvitedpapersaswellasitsgoodorganization. Fromthebeginning, we have sent every paper anonymously to ?ve referees, and we have always accepted only around 50% of the papers sent in. This year it was a little less than that. I would like to thank everybody who helped us by considering Dortmund’s Fuzzy Days as the conference at which to appear. I know that among the - stracts not accepted there were some quite good ones, but we were restricted to a ?xed number. I also know that referees do a good job but cannot always judge wisely from abstracts. Hence my apologies to those who did not make it this year. Please try again! I would like to point out that our conference also has a good regional re- tation. I am grateful to the City of Dortmund, its Lord Mayor Dr. Langemeyer, the Dortmund project, the DFG – Deutsche Forschungsgemeinschaft, the KVR – Kommunalverband Ruhrgebiet, the Martin-Schmeißer-Stiftung, and the C- line AG/Quantum GmbH for their valuable support.
Book Synopsis Combinatorial Optimization and Applications by : Zhao Zhang
Download or read book Combinatorial Optimization and Applications written by Zhao Zhang and published by Springer. This book was released on 2014-11-13 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 8th International Conference on Combinatorial Optimization and Applications, COCOA 2014, held on the island of Maui, Hawaii, USA, in December 2014. The 56 full papers included in the book were carefully reviewed and selected from 133 submissions. Topics covered include classic combinatorial optimization; geometric optimization; network optimization; optimization in graphs; applied optimization; CSoNet; and complexity, cryptography, and games.
Book Synopsis Handbook of Performability Engineering by : Krishna B. Misra
Download or read book Handbook of Performability Engineering written by Krishna B. Misra and published by Springer Science & Business Media. This book was released on 2008-08-24 with total page 1331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dependability and cost effectiveness are primarily seen as instruments for conducting international trade in the free market environment. These factors cannot be considered in isolation of each other. This handbook considers all aspects of performability engineering. The book provides a holistic view of the entire life cycle of activities of the product, along with the associated cost of environmental preservation at each stage, while maximizing the performance.
Book Synopsis Algorithms and Data Structures in VLSI Design by : Christoph Meinel
Download or read book Algorithms and Data Structures in VLSI Design written by Christoph Meinel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the main problems in chip design is the enormous number of possible combinations of individual chip elements within a system, and the problem of their compatibility. The recent application of data structures, efficient algorithms, and ordered binary decision diagrams (OBDDs) has proven vital in designing the computer chips of tomorrow. This book provides an introduction to the foundations of this interdisciplinary research area, emphasizing its applications in computer aided circuit design.
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 Transactions on Petri Nets and Other Models of Concurrency XIII by : Maciej Koutny
Download or read book Transactions on Petri Nets and Other Models of Concurrency XIII written by Maciej Koutny and published by Springer. This book was released on 2018-11-20 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 13th volume of ToPNoC contains revised and extended versions of a selection of the best workshop papers presented at the 38th International Conference on Application and Theory of Petri Nets and Concurrency, Petri Nets 2017, and the 17th International Conference on Application of Concurrency to System Design, ACSD 2017. The 9 papers cover a diverse range of topics including model checking and system verification, refinement, and synthesis; foundational work on specific classes of Petri nets; and innovative applications of Petri nets and other models of concurrency. Application areas covered in this volume are: fault-tolerance, service composition, databases, communication protocols, business processes, and distributed systems. Thus, this volume gives a good overview of ongoing research on concurrent systems and Petri nets.
