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.

Over the years there has been a large increase in the functionality available on a single integrated circuit. This has been mainly achieved by a continuous drive towards smaller feature sizes, larger dies, and better packing efficiency. However, this greater functionality has also resulted in substantial increases in the capital investment needed to build fabrication facilities. Given such a high level of investment, it is critical for IC manufacturers to reduce manufacturing costs and get a better return on their investment. The most obvious method of reducing the manufacturing cost per die is to improve manufacturing yield. Modern VLSI research and engineering (which includes design manufacturing and testing) encompasses a very broad range of disciplines such as chemistry, physics, material science, circuit design, mathematics and computer science. Due to this diversity, the VLSI arena has become fractured into a number of separate sub-domains with little or no interaction between them. This is the case with the relationships between testing and manufacturing. From Contamination to Defects, Faults and Yield Loss: Simulation and Applications focuses on the core of the interface between manufacturing and testing, i.e., the contamination-defect-fault relationship. The understanding of this relationship can lead to better solutions of many manufacturing and testing problems. Failure mechanism models are developed and presented which can be used to accurately estimate probability of different failures for a given IC. This information is critical in solving key yield-related applications such as failure analysis, fault modeling and design manufacturing.

This volume contains a collection of papers presented at the NATO Advanced Study Institute on *Testing and Diagnosis of VLSI and ULSI" held at Villa Olmo, Como (Italy) June 22 -July 3,1987. High Density technologies such as Very-Large Scale Integration (VLSI), Wafer Scale Integration (WSI) and the not-so-far promises of Ultra-Large Scale Integration (ULSI), have exasperated the problema associated with the testing and diagnosis of these devices and systema. Traditional techniques are fast becoming obsolete due to unique requirements such as limited controllability and observability, increasing execution complexity for test vector generation and high cost of fault simulation, to mention just a few. New approaches are imperative to achieve the highly sought goal of the * three months* turn around cycle time for a state-of-the-art computer chip. The importance of testing and diagnostic processes is of primary importance if costs must be kept at acceptable levels. The objective of this NATO-ASI was to present, analyze and discuss the various facets of testing and diagnosis with respect to both theory and practice. The contents of this volume reflect the diversity of approaches currently available to reduce test and diagnosis time. These approaches are described in a concise, yet clear way by renowned experts of the field. Their contributions are aimed at a wide readership: the uninitiated researcher will find the tutorial chapters very rewarding. The expert wiII be introduced to advanced techniques in a very comprehensive manner.

The advent of computer aided design and the proliferation of computer aided design tools have been instrumental in furthering the state-of-the art in integrated circuitry. Continuing this progress, however, demands an emphasis on creating user-friendly environments that facilitate the interaction between the designer and the CAD tool. The realization of this fact has prompted investigations into the appropriateness for CAD of a number of user-interface technologies. One type of interface that has hitherto not been considered is the natural language interface. It is our contention that natural language interfaces could solve many of the problems posed by the increasing number and sophistication of CAD tools. This thesis represents the first step in a research effort directed towards the eventual development of a natural language interface for the domain of computer aided design. The breadth and complexity of the CAD domain renders the task of developing a natural language interface for the complete domain beyond the scope of a single doctoral thesis. Hence, we have initally focussed on a sub-domain of CAD. Specifically, we have developed a natural language interface, named Cleopatra, for circuit-simulation post-processing. In other words, with Cleopatra a circuit-designer can extract and manipulate, in English, values from the output of a circuit-simulator (currently SPICE) without manually having to go through the output files produced by the simulator."

There is a growing social interest in developing vision-based vehicle guidance systems for improving traffic safety and efficiency and the environment. Ex amples of vision-based vehicle guidance systems include collision warning systems, steering control systems for tracking painted lane marks, and speed control systems for preventing rear-end collisions. Like other guidance systems for aircraft and trains, these systems are ex pected to increase traffic safety significantly. For example, safety improve ments of aircraft landing processes after the introduction of automatic guidance systems have been reported to be 100 times better than prior to installment. Although the safety of human lives is beyond price, the cost for automatic guidance could be compensated by decreased insurance costs. It is becoming more important to increase traffic safety by decreasing the human driver's load in our society, especially with an increasing population of senior people who continue to drive. The second potential social benefit is the improvement of traffic efficiency by decreasing the spacing between vehicles without sacrificing safety. It is reported, for example, that four times the efficiency is expected if the spacing between cars is controlled automatically at 90 cm with a speed of 100 kmjh compared to today's typical manual driving. Although there are a lot of tech nical, psychological, and social issues to be solved before realizing the high density jhigh-speed traffic systems described here, highly efficient highways are becoming more important because of increasing traffic congestion."

This book, and the research it describes, resulted from a simple observation we made sometime in 1986. Put simply, we noticed that many VLSI design tools looked "alike." That is, at least at the overall software architecture level, the algorithms and data structures required to solve problem X looked much like those required to solve problem X'. Unfortunately, this resemblance is often of little help in actually writing the software for problem X' given the software for problem X. In the VLSI CAD world, technology changes rapidly enough that design software must continually strive to keep up. And of course, VLSI design software, and engineering design software in general, is often exquisitely sensitive to some aspects of the domain (technology) in which it operates. Modest changes in functionality have an unfortunate tendency to require substantial (and time-consuming) internal software modifications. Now, observing that large engineering software systems are technology dependent is not particularly clever. However, we believe that our approach to xiv Preface dealing with this problem took an interesting new direction. We chose to investigate the extent to which automatic programming ideas cold be used to synthesize such software systems from high-level specifications. This book is one of the results of that effort."

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.

Circuit simulation has been a topic of great interest to the integrated circuit design community for many years. It is a difficult, and interesting, problem be cause circuit simulators are very heavily used, consuming thousands of computer hours every year, and therefore the algorithms must be very efficient. In addi tion, circuit simulators are heavily relied upon, with millions of dollars being gambled on their accuracy, and therefore the algorithms must be very robust. At the University of California, Berkeley, a great deal of research has been devoted to the study of both the numerical properties and the efficient imple mentation of circuit simulation algorithms. Research efforts have led to several programs, starting with CANCER in the 1960's and the enormously successful SPICE program in the early 1970's, to MOTIS-C, SPLICE, and RELAX in the late 1970's, and finally to SPLICE2 and RELAX2 in the 1980's. Our primary goal in writing this book was to present some of the results of our current research on the application of relaxation algorithms to circuit simu lation. As we began, we realized that a large body of mathematical and exper imental results had been amassed over the past twenty years by graduate students, professors, and industry researchers working on circuit simulation. It became a secondary goal to try to find an organization of this mass of material that was mathematically rigorous, had practical relevance, and still retained the natural intuitive simplicity of the circuit simulation subject."

Recently there has been increased interest in the development of computer-aided design programs to support the system level designer of integrated circuits more actively. Such design tools hold the promise of raising the level of abstraction at which an integrated circuit is designed, thus releasing the current designers from many of the details of logic and circuit level design. The promise further suggests that a whole new group of designers in neighboring engineering and science disciplines, with far less understanding of integrated circuit design, will also be able to increase their productivity and the functionality of the systems they design. This promise has been made repeatedly as each new higher level of computer-aided design tool is introduced and has repeatedly fallen short of fulfillment. This book presents the results of research aimed at introducing yet higher levels of design tools that will inch the integrated circuit design community closer to the fulfillment of that promise. 1. 1. SYNTHESIS OF INTEGRATED CmCUITS In the integrated circuit (Ie) design process, a behavior that meets certain specifications is conceived for a system, the behavior is used to produce a design in terms of a set of structural logic elements, and these logic elements are mapped onto physical units. The design process is impacted by a set of constraints as well as technological information (i. e. the logic elements and physical units used for the design).

This volume, which contains 15 contributions, is based on a minicourse held at the 1987 IEEE Plasma Science Meeting. The purpose of the lectures in the course was to acquaint the students with the multidisciplinary nature of computational techniques and the breadth of research areas in plasma science in which computation can address important physics and engineering design issues. These involve: electric and magnetic fields, MHD equations, chemistry, radiation, ionization etc. The contents of the contributions, written subsequent to the minicourse, stress important aspects of computer applications. They are: 1) the numerical methods used; 2) the range of applicability; 3) how the methods are actually employed in research and in the design of devices; and, as a compendium, 4) the multiplicity of approaches possible for any one problem. The materials in this book are organized by both subject and applications which display some of the richness in computational plasma physics.

The roots of the project which culminates with the writing of this book can be traced to the work on logic synthesis started in 1979 at the IBM Watson Research Center and at University of California, Berkeley. During the preliminary phases of these projects, the impor tance of logic minimization for the synthesis of area and performance effective circuits clearly emerged. In 1980, Richard Newton stirred our interest by pointing out new heuristic algorithms for two-level logic minimization and the potential for improving upon existing approaches. In the summer of 1981, the authors organized and participated in a seminar on logic manipulation at IBM Research. One of the goals of the seminar was to study the literature on logic minimization and to look at heuristic algorithms from a fundamental and comparative point of view. The fruits of this investigation were surprisingly abundant: it was apparent from an initial implementation of recursive logic minimiza tion (ESPRESSO-I) that, if we merged our new results into a two-level minimization program, an important step forward in automatic logic synthesis could result. ESPRESSO-II was born and an APL implemen tation was created in the summer of 1982. The results of preliminary tests on a fairly large set of industrial examples were good enough to justify the publication of our algorithms. It is hoped that the strength and speed of our minimizer warrant its Italian name, which denotes both express delivery and a specially-brewed black coffee."

Direct Engineering (DE) is the creation of a product development cycle into a single, unified process. The design process in most industries is an evolutionary one (i.e., incremental changes to some existing design). DE is a manufacturing process that seeks to improve the design processes by providing complete archival documentation of existing designs. It uses three-dimensional geometric models with integrated manufacturing information throughout the design process. DE reduces the design cycle, and the variety and number of engineering changes. This process decreases the design cycle time, increases productivity, and provides a higher quality product. The required technologies and methodologies that will support the development of the DE environment are: (1) product representation using feature-based modeling; (2) knowledge-based applications that will support the entire product development cycle; (3) an engineering environment implemented around distributed computing and object-oriented systems; (4) direct manufacturing techniques using rapid prototyping. Direct Engineering: Toward Intelligent Manufacturing addresses the following recent topics related to the development, implementation, and integration of the DE environment: (1) the current scope of the research in intelligent manufacturing; (2) the results of the technologies and tools developed for integrated product and process designs, and (3) examination of the methodologies and algorithms used for the implementation of direct engineering.

Embedded systems are becoming one of the major driving forces in computer science. Furthermore, it is the impact of embedded information technology that dictates the pace in most engineering domains. Nearly all technical products above a certain level of complexity are not only controlled but increasingly even dominated by their embedded computer systems. Traditionally, such embedded control systems have been implemented in a monolithic, centralized way. Recently, distributed solutions are gaining increasing importance. In this approach, the control task is carried out by a number of controllers distributed over the entire system and connected by some interconnect network, like fieldbuses. Such a distributed embedded system may consist of a few controllers up to several hundred, as in today's top-range automobiles. Distribution and parallelism in embedded systems design increase the engineering challenges and require new development methods and tools. This book is the result of the International Workshop on Distributed and Parallel Embedded Systems (DIPES'98), organized by the International Federation for Information Processing (IFIP) Working Groups 10.3 (Concurrent Systems) and 10.5 (Design and Engineering of Electronic Systems). The workshop took place in October 1998 in Schloss Eringerfeld, near Paderborn, Germany, and the resulting book reflects the most recent points of view of experts from Brazil, Finland, France, Germany, Italy, Portugal, and the USA. The book is organized in six chapters: `Formalisms for Embedded System Design': IP-based system design and various approaches to multi-language formalisms. `Synthesis from Synchronous/Asynchronous Specification': Synthesis techniques based on Message Sequence Charts (MSC), StateCharts, and Predicate/Transition Nets. `Partitioning and Load-Balancing': Application in simulation models and target systems. <`Verification and Validation': Formal techniques for precise verification and more pragmatic approaches to validation. `Design Environments' for distributed embedded systems and their impact on the industrial state of the art. `Object Oriented Approaches': Impact of OO-techniques on distributed embedded systems. GBP/LISTGBP This volume will be essential reading for computer science researchers and application developers.

This book contains the proceedings of the International "Workshop on 3D Process Simulation which was held at the Campus of the University Erlangen-Nuremberg in Erlangen on September 5, 1995, in conjunction with the 6th International Conference on "Simulation of Semiconductor Devices and Processes (SISDEP 95). Whereas two-dimensional semiconductor process simulation has achieved a certain degree of maturity, three-dimensional process simulation is a newly emerging field in which most efforts are dedicated to necessary basic developments. Research in this area is promoted by the growing demand to obtain reliable information on device geometries and dopant distributions needed for three-dimensional device simulation, and challenged by the great algorithmic problems caused by moving interfaces and by the requirement to limit computation times and memory requirements. This workshop provided a forum to discuss the industrial needs, technical problems, and solutions being developed in the field of three-dimensional semiconductor process simulation. Invited presentations from leading semiconductor companies and research Centers of Excellence from Japan, the USA, and Europe outlined novel numerical algorithms, physical models, and applications in this rapidly emerging field.

Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi- particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.

In the last few decades, multiscale algorithms have become a dominant trend in large-scale scientific computation. Researchers have successfully applied these methods to a wide range of simulation and optimization problems. This book gives a general overview of multiscale algorithms; applications to general combinatorial optimization problems such as graph partitioning and the traveling salesman problem; and VLSICAD applications, including circuit partitioning, placement, and VLSI routing. Additional chapters discuss optimization in reconfigurable computing, convergence in multilevel optimization, and model problems with PDE constraints.

Audience Written at the graduate level, the book is intended for engineers and mathematical and computational scientists studying large-scale optimization in electronic design automation.

The "Fifth International Conference on Simulation of Semiconductor Devices and Processes" (SISDEP 93) continues a series of conferences which was initiated in 1984 by K. Board and D. R. J. Owen at the University College of Wales, Swansea, where it took place a second time in 1986. Its organization was succeeded by G. Baccarani and M. Rudan at the University of Bologna in 1988, and W. Fichtner and D. Aemmer at the Federal Institute of Technology in Zurich in 1991. This year the conference is held at the Technical University of Vienna, Austria, September 7 - 9, 1993. This conference shall provide an international forum for the presentation of out standing research and development results in the area of numerical process and de vice simulation. The miniaturization of today's semiconductor devices, the usage of new materials and advanced process steps in the development of new semiconduc tor technologies suggests the design of new computer programs. This trend towards more complex structures and increasingly sophisticated processes demands advanced simulators, such as fully three-dimensional tools for almost arbitrarily complicated geometries. With the increasing need for better models and improved understand ing of physical effects, the Conference on Simulation of Semiconductor Devices and Processes brings together the simulation community and the process- and device en gineers who need reliable numerical simulation tools for characterization, prediction, and development."

This handbook provides design considerations and rules-of-thumb to ensure the functionality you want will work. It brings together all the information needed by systems designers to develop applications that include configurability, from the simplest implementations to the most complicated.

The area of computer graphics is characterized by rapid evolution. New techniques in hardware and software developments, e. g., new rendering methods, have led to new ap plications and broader acceptance of graphics in fields such as scientific visualization, multi-media applications, computer aided design, and virtual reality systems. The evolving functionality and the growing complexity of graphics algorithms and sys tems make it more difficult for the application programmer to take full advantage of these systems. Conventional programming methods are no longer suited to manage the increasing complexity, so new programming paradigms and system architectures are re quired. One important step in this direction is the introduction and use of object-oriented methods. Intuition teils us that visible graphical entities are objects, and experience has indeed shown that object-oriented software techniques are quite useful for graphics. The expressiveness of object-oriented languages compared to pure procedurallanguages gives the graphics application programmer much better support when transforming his mental intentions into computer code. Moreover, object-oriented software development is a, weil founded technology, allowing software to be built from reusable and extensible compo nents. This book contains selected, reviewed and thoroughly revised vers ions of papers submit ted to and presented at the Fourth Eurographies Workshops on Object-Oriented Graphics, held on May 9-11, 1994 in Sintra, Portugal."

Our purpose in writing this book was two-fold. First, we wanted to compile a chronology of the research in the field of mixed-mode simulation over the last ten to fifteen years. A substantial amount of work was done during this period of time but most of it was published in archival form in Masters theses and Ph. D. dissertations. Since the interest in mixed-mode simulation is growing, and a thorough review of the state-of-the-art in the area was not readily available, we thought it appropriate to publish the information in the form of a book. Secondly, we wanted to provide enough information to the reader so that a proto type mixed-mode simulator could be developed using the algorithms in this book. The SPLICE family of programs is based on the algorithms and techniques described in this book and so it can also serve as docu mentation for these programs. ACKNOWLEDGEMENTS The authors would like to dedicate this book to Prof. D. O. Peder son for inspiring this research work and for providing many years of support and encouragement The authors enjoyed many fruitful discus sions and collaborations with Jim Kleckner, Young Kim, Alberto Sangiovanni-Vincentelli, and Jacob White, and we thank them for their contributions. We also thank the countless others who participated in the research work and read early versions of this book. Lillian Beck provided many useful suggestions to improve the manuscript. Yun cheng Ju did the artwork for the illustrations."

This volume presents the proceedings of the 7th International Confer ence of the Computer Graphics Society, CG International '89, held at the University of Leeds, UK, June 27-30, 1989. Since 1982 this confer ence has continued to attract high-quality research papers in all aspects of computer graphics and its applications. Originally the conference was held in Japan (1982-1987), but in 1988 was held in Geneva, Switzerland. Future conferences are planned for Singapore in 1990, USA in 1991, Japan in 1992, and Canada in 1993. Recent developments in computer graphics have concentrated on the following: greater sophistication of image generation techniques; advances in hardware and emphasis on the exploitation of parallelism, integration of robotics and AI techniques for animation, greater integ ration of CAD and CAM in CIM, use of powerful computer graphics techniques to represent complex physical processes (visualization), advances in computational geometry and in the representation and modelling of complex physical and mathematical objects, and improved tools and methods for HC . These trends and advances are reflected in this present volume. A number of papers deal with important research aspects in many of these areas."

Complex Automated Negotiations have been widely studied and are becoming an important, emerging area in the field of Autonomous Agents and Multi-Agent Systems. In general, automated negotiations can be complex, since there are a lot of factors that characterize such negotiations. These factors include the number of issues, dependency between issues, representation of utility, negotiation protocol, negotiation form (bilateral or multi-party), time constraints, etc. Software agents can support automation or simulation of such complex negotiations on the behalf of their owners, and can provide them with adequate bargaining strategies. In many multi-issue bargaining settings, negotiation becomes more than a zero-sum game, so bargaining agents have an incentive to cooperate in order to achieve efficient win-win agreements. Also, in a complex negotiation, there could be multiple issues that are interdependent. Thus, agent's utility will become more complex than simple utility functions. Further, negotiation forms and protocols could be different between bilateral situations and multi-party situations. To realize such a complex automated negotiation, we have to incorporate advanced Artificial Intelligence technologies includes search, CSP, graphical utility models, Bays nets, auctions, utility graphs, predicting and learning methods. Applications could include e-commerce tools, decision-making support tools, negotiation support tools, collaboration tools, etc. In this book, we solicit papers on all aspects of such complex automated negotiations in the field of Autonomous Agents and Multi-Agent Systems. In addition, this book includes papers on the ANAC 2010 (Automated Negotiating Agents Competition), in which automated agents who have different negotiation strategies and implemented by different developers are automatically negotiate in the several negotiation domains. ANAC is one of real testbeds in which strategies for automated negotiating agents are evaluated in a tournament style.

Informationssysteme sind die Grundlage von Building Information Modelling, BIM. Vernetzte Informationen und durchgangig vernetzte Modelldaten sind die Grundlage partnerschaftlichen Bauens. Sie erlauben transparentes Controlling und zuverlassiges Risikomanagement. Multimodelle sind vernetzte Informationen. Die Grundlagen und Methoden von BIM und Multimodellen werden erlautert und es wird aufgezeigt, wie ein prozessorientiertes Management mit Multimodellen neue Qualitat in die Planung und Steuerung von Bauprozessen bringt. Die durchgehende BIM Arbeitsweise mit vernetzten Informationen erlaubt Bauablaufsimulationen in kurzester Zeit durchzufuhren. Neben dem virtuellen Bauwerk wird auch eine virtuelle Baustelle virtuelle Realitat und gibt wichtige neue Eindrucke fur das Baumanagement. Baumanagementinformationen werden auf einmal transparent, erfassbar, begreifbar. Band 1 konzentriert sich auf die Grundlagen der Modelle und ihre Erweiterung durch Linkmodelle, auf die Methoden fur BIM und Multimodelldaten wie das Filtern, das Visualisieren und auf die Prozesse, ihre schnelle Konfiguration und das prozessbasierte Planen und Managen sowie die Informationslogistik, die gerade durch Multimodelle neue Ansatze und Qualitaten erhalt, wahrend Band 2 anschauliche Anwendungen in Baustellenplanung, Bauablaufsimulation, Bauprojekt- und Risikomanagement aufzeigt.

This unique book deals with the migration of existing hard IP from one technology to another, using repeatable procedures. It will allow CAD practitioners to quickly develop methodologies that capitalize on the large volumes of legacy data available within a company today.

mental improvements during the same period. What is clearly needed in verification techniques and technology is the equivalent of a synthesis productivity breakthrough. In the second edition of Writing Testbenches, Bergeron raises the verification level of abstraction by introducing coverage-driven constrained-random transaction-level self-checking testbenches all made possible through the introduction of hardware verification languages (HVLs), such as e from Verisity and OpenVera from Synopsys. The state-of-art methodologies described in Writing Test benches will contribute greatly to the much-needed equivalent of a synthesis breakthrough in verification productivity. I not only highly recommend this book, but also I think it should be required reading by anyone involved in design and verification of today's ASIC, SoCs and systems. Harry Foster Chief Architect Verplex Systems, Inc. xviii Writing Testbenches: Functional Verification of HDL Models PREFACE If you survey hardware design groups, you will learn that between 60% and 80% of their effort is now dedicated to verification.