Alberto L. Sangiovanni-Vincentelli

Synthesis of Finite State Machines: Logic Optimization is the second in a set of two monographs devoted to the synthesis of Finite State Machines (FSMs). The first volume, Synthesis of Finite State Machines: Functional Optimization, addresses functional optimization, whereas this one addresses logic optimization. The result of functional optimization is a symbolic description of an FSM which represents a sequential function chosen from a collection of permissible candidates. Logic optimization is the body of techniques for converting a symbolic description of an FSM into a hardware implementation. The mapping of a given symbolic representation into a two-valued logic implementation is called state encoding (or state assignment) and it impacts heavily area, speed, testability and power consumption of the realized circuit. The first part of the book introduces the relevant background, presents results previously scattered in the literature on the computational complexity of encoding problems, and surveys in depth old and new approaches to encoding in logic synthesis. The second part of the book presents two main results about symbolic minimization; a new procedure to find minimal two-level symbolic covers, under face, dominance and disjunctive constraints, and a unified frame to check encodability of encoding constraints and find codes of minimum length that satisfy them. The third part of the book introduces generalized prime implicants (GPIs), which are the counterpart, in symbolic minimization of two-level logic, to prime implicants in two-valued two-level minimization. GPIs enable the design of an exact procedure for two-level symbolic minimization, based on a covering step which is complicated by the need to guarantee encodability of the final cover. A new efficient algorithm to verify encodability of a selected cover is presented. If a cover is not encodable, it is shown how to augment itminimally until an encodable superset of GPIs is determined. To handle encodability the authors have extended the frame to satisfy encoding constraints presented in the second part. The covering problems generated in the minimization of GPIs tend to be very large. Recently large covering problems have been attacked successfully by representing the covering table with binary decision diagrams (BDD). In the fourth part of the book the authors introduce such techniques and extend them to the case of the implicit minimization of GPIs, where the encodability and augmentation steps are also performed implicitly. Synthesis of Finite State Machines: Logic Optimization will be of interest to researchers and professional engineers who work in the area of computer-aided design of integrated circuits.

Synthesis of Finite State Machines: Functional Optimization is one of two monographs devoted to the synthesis of Finite State Machines (FSMs). This volume addresses functional optimization, whereas the second addresses logic optimization. By functional optimization here we mean the body of techniques that: compute all permissible sequential functions for a given topology of interconnected FSMs, and select a `best' sequential function out of the permissible ones. The result is a symbolic description of the FSM representing the chosen sequential function. By logic optimization here we mean the steps that convert a symbolic description of an FSM into a hardware implementation, with the goal to optimize objectives like area, testability, performance and so on. Synthesis of Finite State Machines: Functional Optimization is divided into three parts. The first part presents some preliminary definitions, theories and techniques related to the exploration of behaviors of FSMs. The second part presents an implicit algorithm for exact state minimization of incompletely specified finite state machines (ISFSMs), and an exhaustive presentation of explicit and implicit algorithms for the binate covering problem. The third part addresses the computation of permissible behaviors at a node of a network of FSMs and the related minimization problems of non-deterministic finite state machines (NDFSMs). Key themes running through the book are the exploration of behaviors contained in a non-deterministic FSM (NDFSM), and the representation of combinatorial problems arising in FSM synthesis by means of Binary Decision Diagrams (BDDs). Synthesis of Finite State Machines: Functional Optimization will be of interest to researchers and designers in logic synthesis, CAD and design automation.

Synthesis of Finite State Machines: Logic Optimization is the second in a set of two monographs devoted to the synthesis of Finite State Machines (FSMs). The first volume, Synthesis of Finite State Machines: Functional Optimization, addresses functional optimization, whereas this one addresses logic optimization. The result of functional optimization is a symbolic description of an FSM which represents a sequential function chosen from a collection of permissible candidates. Logic optimization is the body of techniques for converting a symbolic description of an FSM into a hardware implementation. The mapping of a given symbolic representation into a two-valued logic implementation is called state encoding (or state assignment) and it impacts heavily area, speed, testability and power consumption of the realized circuit. The first part of the book introduces the relevant background, presents results previously scattered in the literature on the computational complexity of encoding problems, and surveys in depth old and new approaches to encoding in logic synthesis. The second part of the book presents two main results about symbolic minimization; a new procedure to find minimal two-level symbolic covers, under face, dominance and disjunctive constraints, and a unified frame to check encodability of encoding constraints and find codes of minimum length that satisfy them. The third part of the book introduces generalized prime implicants (GPIs), which are the counterpart, in symbolic minimization of two-level logic, to prime implicants in two-valued two-level minimization. GPIs enable the design of an exact procedure for two-level symbolic minimization, based on a covering step which is complicated by the need to guarantee encodability of the final cover. A new efficient algorithm to verify encodability of a selected cover is presented. If a cover is not encodable, it is shown how to augment itminimally until an encodable superset of GPIs is determined. To handle encodability the authors have extended the frame to satisfy encoding constraints presented in the second part. The covering problems generated in the minimization of GPIs tend to be very large. Recently large covering problems have been attacked successfully by representing the covering table with binary decision diagrams (BDD). In the fourth part of the book the authors introduce such techniques and extend them to the case of the implicit minimization of GPIs, where the encodability and augmentation steps are also performed implicitly. Synthesis of Finite State Machines: Logic Optimization will be of interest to researchers and professional engineers who work in the area of computer-aided design of integrated circuits.

Synthesis of Finite State Machines: Functional Optimization is one of two monographs devoted to the synthesis of Finite State Machines (FSMs). This volume addresses functional optimization, whereas the second addresses logic optimization. By functional optimization here we mean the body of techniques that: compute all permissible sequential functions for a given topology of interconnected FSMs, and select a `best' sequential function out of the permissible ones. The result is a symbolic description of the FSM representing the chosen sequential function. By logic optimization here we mean the steps that convert a symbolic description of an FSM into a hardware implementation, with the goal to optimize objectives like area, testability, performance and so on. Synthesis of Finite State Machines: Functional Optimization is divided into three parts. The first part presents some preliminary definitions, theories and techniques related to the exploration of behaviors of FSMs. The second part presents an implicit algorithm for exact state minimization of incompletely specified finite state machines (ISFSMs), and an exhaustive presentation of explicit and implicit algorithms for the binate covering problem. The third part addresses the computation of permissible behaviors at a node of a network of FSMs and the related minimization problems of non-deterministic finite state machines (NDFSMs). Key themes running through the book are the exploration of behaviors contained in a non-deterministic FSM (NDFSM), and the representation of combinatorial problems arising in FSM synthesis by means of Binary Decision Diagrams (BDDs). Synthesis of Finite State Machines: Functional Optimization will be of interest to researchers and designers in logic synthesis, CAD and design automation.

An embedded system is loosely defined as any system that utilizes electronics but is not perceived or used as a general-purpose computer. Traditionally, one or more electronic circuits or microprocessors are literally embedded in the system, either taking up roles that used to be performed by mechanical devices, or providing functionality that is not otherwise possible. The goal of this book is to investigate how formal methods can be applied to the domain of embedded system design. The emphasis is on the specification, representation, validation, and design exploration of such systems from a high-level perspective. The authors review the framework upon which the theories and experiments are based, and through which the formal methods are linked to synthesis and simulation. A formal verification methodology is formulated to verify general properties of the designs and demonstrate that this methodology is efficient in dealing with the problem of complexity and effective in finding bugs. However, manual intervention in the form of abstraction selection and separation of timing and functionality is required. It is conjectured that, for specific properties, efficient algorithms exist for completely automatic formal validations of systems. Synchronous Equivalence: Formal Methods for Embedded Systems presents a brand new formal approach to high-level equivalence analysis. It opens design exploration avenues previously uncharted. It is a work that can stand alone but at the same time is fully compatible with the synthesis and simulation framework described in another book by Kluwer Academic Publishers Hardware-Software Co-Design of Embedded Systems: The POLIS Approach, by Balarin et al. Synchronous Equivalence: Formal Methods for Embedded Systems will be of interest to embedded system designers (automotive electronics, consumer electronics, and telecommunications), micro-controller designers, CAD developers and students, as well as IP providers, architecture platform designers, operating system providers, and designers of VLSI circuits and systems.

This book was motivated by the problems being faced with shrinking IC process feature sizes. It is well known that as process feature sizes shrink, a host of electrical problems like cross-talk, electromigration, self-heat, etc. are becoming important. Cross-talk is one of the major problems since it results in unpredictable design behavior. In particular, it can result in significant delay variation or signal integrity problems in a wire, depending on the state of its neighboring wires. Typical approaches to tackle the cross-talk problem attempt to fix the problem once it is created. In our approach, we ensure that cross-talk is eliminated by design. The work described in this book attempts to take an "outside-the-box" view and propose a radically different design style. This design style first imposes a fixed layout pattern (or fabric) on the integrated circuit, and then embeds the circuit being implemented into this fabric. The fabric is chosen carefully in order to eliminate the cross-talk problem being faced in modem IC processes. With our choice of fabric, cross-talk between adjacent wires on an IC is reduced by between one and two orders of magnitude. In this way, the fabric concept eliminates cross-talk up-front, and by design. We propose two separate design flows, each of which uses the fabric concept to implement logic. The first flow uses fabric-compliant standard cells as an im­ plementation vehicle. We call these cells fabric cells, and they have the same logic functionality as existing standard cells with which they are compared.

Function Architecture Co-Design is a new paradigm for the design and implementation of embedded systems. Function/Architecture Optimization and Co-Design of Embedded Systems presents the authors' work in developing a function/architecture optimization and co-design formal methodology and framework for control-dominated embedded systems. The approach incorporates both data flow and control optimizations performed on a suitable novel intermediate design task representation. The aim is not only to enhance productivity of the designer and system developer, but also to improve quality of the final synthesis outcome. Function/Architecture Optimization and Co-Design of Embedded Systems discusses the proposed function/architecture co-design methodology, focusing on design representation, optimization, validation, and synthesis. Throughout the text, the difference between behavior specification and implementation is emphasized. The current need in co-design to move from synthesis-based technology to compiler-based technology is pointed out. The authors describe and show how performing data flow and control optimizations at the high abstraction level can lead to significant size and performance improvements in both the synthesized hardware and software. The work builds on bodies of research in the silicon and software compilation domains. The aforementioned techniques are specialized to the embedded systems domain. It is recognized that guided optimization can be applied on the internal design representation, no matter what the abstraction level, and need not be restricted to the final stages of software assembly code generation, or hardware synthesis. Function/Architecture Optimization and Co-Design of Embedded Systems will be of primary interest to researchers, developers, and professionals in the field of embedded systems design.

Short turnaround has become critical in the design of electronic systems. Software- programmable components such as microprocessors and digital signal processors have been used extensively in such systems since they allow rapid design revisions. However, the inherent performance limitations of software-programmable systems mean that they are inadequate for high-performance designs. Designers thus turned to gate arrays as a solution. User-programmable gate arrays (field-programmable gate arrays, FPGAs) have recently emerged and are changing the way electronic systems are designed and implemented. The growing complexity of the logic circuits that can be packed onto an FPGA chip means that it has become important to have automatic synthesis tools that implement logic functions on these architectures. Logic Synthesis for Field-Programmable Gate Arrays describes logic synthesis for both look-up table (LUT) and multiplexor-based architectures, with a balanced presentation of existing techniques together with algorithms and the system developed by the authors. Audience: A useful reference for VLSI designers, developers of computer-aided design tools, and anyone involved in or with FPGAs.

Since the second half of the 1980s asynchronous circuits have been the subject of a great deal of research following a period of relative oblivion. The lack of interest in asynchronous techniques was motivated by the progressive shift towards synchronous design techniques that had much more structure and were much easier to verify and synthesize. System design requirements made it impossible to eliminate totally the use of asynchronous circuits. Given the objective difficulty encountered by designers, the asynchronous components of electronic systems such as interfaces became a serious bottleneck in the design process. The use of new models and some theoretical breakthroughs made it possible to develop asynchronous design techniques that were reliable and effective. This book describes a variety of mathematical models and of algorithms that form the backbone and the body of a new design methodology for asyn­ chronous design. The book is intended for asynchronous hardware designers, for computer-aided tool experts, and for digital designers interested in ex­ ploring the possibility of designing asynchronous circuits. It requires a solid mathematical background in discrete event systems and algorithms. While the book has not been written as a textbook, nevertheless it could be used as a reference book in an advanced course in logic synthesis or asynchronous design.

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.

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.

The motivation for starting the work described in this book was the interest that Hewlett-Packard's microwave circuit designers had in simulation techniques that could tackle the problem of finding steady­ state solutions for nonlinear circuits, particularly circuits containing distributed elements such as transmission lines. Examining the problem of computing steady-state solutions in this context has led to a collection of novel numerical algorithms which we have gathered, along with some background material, into this book. Although we wished to appeal to as broad an audience as possible, to treat the subject in depth required maintaining a narrow focus. Our compromise was to assume that the reader is familiar with basic numerical methods, such as might be found in [dahlquist74] or [vlach83], but not assume any specialized knowledge of methods for steady-state problems. Although we focus on algorithms for computing steady-state solutions of analog and microwave circuits, the methods herein are general in nature and may find use in other disciplines. A number of new algorithms are presented, the contributions primarily centering around new approaches to harmonic balance and mixed frequency-time methods. These methods are described, along with appropriate background material, in what we hope is a reasonably satisfying blend of theory, practice, and results. The theory is given so that the algorithms can be fully understood and their correctness established.

In this book, we concentrate on developing noise simulation techniques for RF circuits. The difference between our approach of performing noise analysis for RF circuits and the traditional techniques is that we first concentrate on the noise analysis for oscillators instead of non-oscillatory circuits. As a first step, we develop a new quantitative description of the dynamics of stable nonlinear oscillators in presence of deterministic perturbations. Unlike previous such attempts, this description is not limited to two-dimensional system of equations and does not make any assumptions about the type of nonlinearity. By considering stochastic perturbations in a stochastic differential calculus setting, we obtain a correct mathematical characterization of the noisy oscillator output. We present efficient numerical techniques both in time domain and in frequency domain for computing the phase noise of oscillators. This approach also determines the relative contribution of the device noise sources to phase noise, which is very useful for oscillator design.

In this book, we concentrate on developing noise simulation techniques for RF circuits. The difference between our approach of performing noise analysis for RF circuits and the traditional techniques is that we first concentrate on the noise analysis for oscillators instead of non-oscillatory circuits. As a first step, we develop a new quantitative description of the dynamics of stable nonlinear oscillators in presence of deterministic perturbations. Unlike previous such attempts, this description is not limited to two-dimensional system of equations and does not make any assumptions about the type of nonlinearity. By considering stochastic perturbations in a stochastic differential calculus setting, we obtain a correct mathematical characterization of the noisy oscillator output. We present efficient numerical techniques both in time domain and in frequency domain for computing the phase noise of oscillators. This approach also determines the relative contribution of the device noise sources to phase noise, which is very useful for oscillator design.

This book was motivated by the problems being faced with shrinking IC process feature sizes. It is well known that as process feature sizes shrink, a host of electrical problems like cross-talk, electromigration, self-heat, etc. are becoming important. Cross-talk is one of the major problems since it results in unpredictable design behavior. In particular, it can result in significant delay variation or signal integrity problems in a wire, depending on the state of its neighboring wires. Typical approaches to tackle the cross-talk problem attempt to fix the problem once it is created. In our approach, we ensure that cross-talk is eliminated by design. The work described in this book attempts to take an "outside-the-box" view and propose a radically different design style. This design style first imposes a fixed layout pattern (or fabric) on the integrated circuit, and then embeds the circuit being implemented into this fabric. The fabric is chosen carefully in order to eliminate the cross-talk problem being faced in modem IC processes. With our choice of fabric, cross-talk between adjacent wires on an IC is reduced by between one and two orders of magnitude. In this way, the fabric concept eliminates cross-talk up-front, and by design. We propose two separate design flows, each of which uses the fabric concept to implement logic. The first flow uses fabric-compliant standard cells as an im­ plementation vehicle. We call these cells fabric cells, and they have the same logic functionality as existing standard cells with which they are compared.

An embedded system is loosely defined as any system that utilizes electronics but is not perceived or used as a general-purpose computer. Traditionally, one or more electronic circuits or microprocessors are literally embedded in the system, either taking up roles that used to be performed by mechanical devices, or providing functionality that is not otherwise possible. The goal of this book is to investigate how formal methods can be applied to the domain of embedded system design. The emphasis is on the specification, representation, validation, and design exploration of such systems from a high-level perspective. The authors review the framework upon which the theories and experiments are based, and through which the formal methods are linked to synthesis and simulation. A formal verification methodology is formulated to verify general properties of the designs and demonstrate that this methodology is efficient in dealing with the problem of complexity and effective in finding bugs. However, manual intervention in the form of abstraction selection and separation of timing and functionality is required. It is conjectured that, for specific properties, efficient algorithms exist for completely automatic formal validations of systems. Synchronous Equivalence: Formal Methods for Embedded Systems presents a brand new formal approach to high-level equivalence analysis. It opens design exploration avenues previously uncharted. It is a work that can stand alone but at the same time is fully compatible with the synthesis and simulation framework described in another book by Kluwer Academic Publishers Hardware-Software Co-Design of Embedded Systems: The POLIS Approach, by Balarin et al. Synchronous Equivalence: Formal Methods for Embedded Systems will be of interest to embedded system designers (automotive electronics, consumer electronics, and telecommunications), micro-controller designers, CAD developers and students, as well as IP providers, architecture platform designers, operating system providers, and designers of VLSI circuits and systems.

Function Architecture Co-Design is a new paradigm for the design and implementation of embedded systems. Function/Architecture Optimization and Co-Design of Embedded Systems presents the authors' work in developing a function/architecture optimization and co-design formal methodology and framework for control-dominated embedded systems. The approach incorporates both data flow and control optimizations performed on a suitable novel intermediate design task representation. The aim is not only to enhance productivity of the designer and system developer, but also to improve quality of the final synthesis outcome. Function/Architecture Optimization and Co-Design of Embedded Systems discusses the proposed function/architecture co-design methodology, focusing on design representation, optimization, validation, and synthesis. Throughout the text, the difference between behavior specification and implementation is emphasized. The current need in co-design to move from synthesis-based technology to compiler-based technology is pointed out. The authors describe and show how performing data flow and control optimizations at the high abstraction level can lead to significant size and performance improvements in both the synthesized hardware and software. The work builds on bodies of research in the silicon and software compilation domains. The aforementioned techniques are specialized to the embedded systems domain. It is recognized that guided optimization can be applied on the internal design representation, no matter what the abstraction level, and need not be restricted to the final stages of software assembly code generation, or hardware synthesis. Function/Architecture Optimization and Co-Design of Embedded Systems will be of primary interest to researchers, developers, and professionals in the field of embedded systems design.

Short turnaround has become critical in the design of electronic systems. Software- programmable components such as microprocessors and digital signal processors have been used extensively in such systems since they allow rapid design revisions. However, the inherent performance limitations of software-programmable systems mean that they are inadequate for high-performance designs. Designers thus turned to gate arrays as a solution. User-programmable gate arrays (field-programmable gate arrays, FPGAs) have recently emerged and are changing the way electronic systems are designed and implemented. The growing complexity of the logic circuits that can be packed onto an FPGA chip means that it has become important to have automatic synthesis tools that implement logic functions on these architectures. Logic Synthesis for Field-Programmable Gate Arrays describes logic synthesis for both look-up table (LUT) and multiplexor-based architectures, with a balanced presentation of existing techniques together with algorithms and the system developed by the authors. Audience: A useful reference for VLSI designers, developers of computer-aided design tools, and anyone involved in or with FPGAs.

Since the second half of the 1980s asynchronous circuits have been the subject of a great deal of research following a period of relative oblivion. The lack of interest in asynchronous techniques was motivated by the progressive shift towards synchronous design techniques that had much more structure and were much easier to verify and synthesize. System design requirements made it impossible to eliminate totally the use of asynchronous circuits. Given the objective difficulty encountered by designers, the asynchronous components of electronic systems such as interfaces became a serious bottleneck in the design process. The use of new models and some theoretical breakthroughs made it possible to develop asynchronous design techniques that were reliable and effective. This book describes a variety of mathematical models and of algorithms that form the backbone and the body of a new design methodology for asyn­ chronous design. The book is intended for asynchronous hardware designers, for computer-aided tool experts, and for digital designers interested in ex­ ploring the possibility of designing asynchronous circuits. It requires a solid mathematical background in discrete event systems and algorithms. While the book has not been written as a textbook, nevertheless it could be used as a reference book in an advanced course in logic synthesis or asynchronous design.

The motivation for starting the work described in this book was the interest that Hewlett-Packard's microwave circuit designers had in simulation techniques that could tackle the problem of finding steady­ state solutions for nonlinear circuits, particularly circuits containing distributed elements such as transmission lines. Examining the problem of computing steady-state solutions in this context has led to a collection of novel numerical algorithms which we have gathered, along with some background material, into this book. Although we wished to appeal to as broad an audience as possible, to treat the subject in depth required maintaining a narrow focus. Our compromise was to assume that the reader is familiar with basic numerical methods, such as might be found in [dahlquist74] or [vlach83], but not assume any specialized knowledge of methods for steady-state problems. Although we focus on algorithms for computing steady-state solutions of analog and microwave circuits, the methods herein are general in nature and may find use in other disciplines. A number of new algorithms are presented, the contributions primarily centering around new approaches to harmonic balance and mixed frequency-time methods. These methods are described, along with appropriate background material, in what we hope is a reasonably satisfying blend of theory, practice, and results. The theory is given so that the algorithms can be fully understood and their correctness established.