Moore's law [Noy77], which predicted that the number of devices in tegrated on a chip would be doubled every two years, was accurate for a number of years. Only recently has the level of integration be gun to slow down somewhat due to the physical limits of integration technology. Advances in silicon technology have allowed Ie design ers to integrate more than a few million transistors on a chip; even a whole system of moderate complexity can now be implemented on a single chip. To keep pace with the increasing complexity in very large scale integrated (VLSI) circuits, the productivity of chip designers would have to increase at the same rate as the level of integration. Without such an increase in productivity, the design of complex systems might not be achievable within a reasonable time-frame. The rapidly increasing complexity of VLSI circuits has made de- 1 2 INTRODUCTION sign automation an absolute necessity, since the required increase in productivity can only be accomplished with the use of sophisticated design tools. Such tools also enable designers to perform trade-off analyses of different logic implementations and to make well-informed design decisions.

Moore's law [Noy77], which predicted that the number of devices in tegrated on a chip would be doubled every two years, was accurate for a number of years. Only recently has the level of integration be gun to slow down somewhat due to the physical limits of integration technology. Advances in silicon technology have allowed Ie design ers to integrate more than a few million transistors on a chip; even a whole system of moderate complexity can now be implemented on a single chip. To keep pace with the increasing complexity in very large scale integrated (VLSI) circuits, the productivity of chip designers would have to increase at the same rate as the level of integration. Without such an increase in productivity, the design of complex systems might not be achievable within a reasonable time-frame. The rapidly increasing complexity of VLSI circuits has made de- 1 2 INTRODUCTION sign automation an absolute necessity, since the required increase in productivity can only be accomplished with the use of sophisticated design tools. Such tools also enable designers to perform trade-off analyses of different logic implementations and to make well-informed design decisions.

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.

Designing VLSI systems represents a challenging task. It is a transfonnation among different specifications corresponding to different levels of design: abstraction, behavioral, stntctural and physical. The behavioral level describes the functionality of the design. It consists of two components; static and dynamic. The static component describes operations, whereas the dynamic component describes sequencing and timing. The structural level contains infonnation about components, control and connectivity. The physical level describes the constraints that should be imposed on the floor plan, the placement of components, and the geometry of the design. Constraints of area, speed and power are also applied at this level. To implement such multilevel transfonnation, a design methodology should be devised, taking into consideration the constraints, limitations and properties of each level. The mapping process between any of these domains is non-isomorphic. A single behavioral component may be transfonned into more than one structural component. Design methodologies are the most recent evolution in the design automation era, which started off with the introduction and subsequent usage of module generation especially for regular structures such as PLA's and memories. A design methodology should offer an integrated design system rather than a set of separate unrelated routines and tools. A general outline of a desired integrated design system is as follows: * Decide on a certain unified framework for all design levels. * Derive a design method based on this framework. * Create a design environment to implement this design method.

An Analog VLSI System for Stereoscopic Vision investigates the interaction of the physical medium and the computation in both biological and analog VLSI systems by synthesizing a functional neuromorphic system in silicon. In both the synthesis and analysis of the system, a point of view from within the system is adopted rather than that of an omniscient designer drawing a blueprint. This perspective projects the design and the designer into a living landscape. The motivation for a machine-centered perspective is explained in the first chapter. The second chapter describes the evolution of the silicon retina. The retina accurately encodes visual information over orders of magnitude of ambient illumination, using mismatched components that are calibrated as part of the encoding process. The visual abstraction created by the retina is suitable for transmission through a limited bandwidth channel. The third chapter introduces a general method for interchip communication, the address-event representation, which is used for transmission of retinal data. The address-event representation takes advantage of the speed of CMOS relative to biological neurons to preserve the information of biological action potentials using digital circuitry in place of axons. The fourth chapter describes a collective circuit that computes stereodisparity. In this circuit, the processing that corrects for imperfections in the hardware compensates for inherent ambiguity in the environment. The fifth chapter demonstrates a primitive working stereovision system. An Analog VLSI System for Stereoscopic Vision contributes to both computer engineering and neuroscience at a concrete level. Through the construction of a working analog of biological vision subsystems, new circuits for building brain-style analog computers have been developed. Specific neuropysiological and psychophysical results in terms of underlying electronic mechanisms are explained. These examples demonstrate the utility of using biological principles for building brain-style computers and the significance of building brain-style computers for understanding the nervous system.

Logic Synthesis and Optimization presents up-to-date research information in a pedagogical form. The authors are recognized as the leading experts on the subject. The focus of the book is on logic minimization and includes such topics as two-level minimization, multi-level minimization, application of binary decision diagrams, delay optimization, asynchronous circuits, spectral method for logic design, field programmable gate array (FPGA) design, EXOR logic synthesis and technology mapping. Examples and illustrations are included so that each contribution can be read independently. Logic Synthesis and Optimization is an indispensable reference for academic researchers as well as professional CAD engineers.

Statistical timing analysis is an area of growing importance in nanometer te- nologies‚ as the uncertainties associated with process and environmental var- tions increase‚ and this chapter has captured some of the major efforts in this area. This remains a very active field of research‚ and there is likely to be a great deal of new research to be found in conferences and journals after this book is published. In addition to the statistical analysis of combinational circuits‚ a good deal of work has been carried out in analyzing the effect of variations on clock skew. Although we will not treat this subject in this book‚ the reader is referred to [LNPS00‚ HN01‚ JH01‚ ABZ03a] for details. 7 TIMING ANALYSIS FOR SEQUENTIAL CIRCUITS 7.1 INTRODUCTION A general sequential circuit is a network of computational nodes (gates) and memory elements (registers). The computational nodes may be conceptualized as being clustered together in an acyclic network of gates that forms a c- binational logic circuit. A cyclic path in the direction of signal propagation 1 is permitted in the sequential circuit only if it contains at least one register . In general, it is possible to represent any sequential circuit in terms of the schematic shown in Figure 7.1, which has I inputs, O outputs and M registers. The registers outputs feed into the combinational logic which, in turn, feeds the register inputs. Thus, the combinational logic has I + M inputs and O + M outputs.