Spectral Techniques in VLSI CAD have become a subject of renewed interest in the design automation community due to the emergence of new and efficient methods for the computation of discrete function spectra. In the past, spectral computations for digital logic were too complex for practical implementation. The use of decision diagrams for spectral computations has greatly reduced this obstacle allowing for the development of new and useful spectral techniques for VLSI synthesis and verification. Several new algorithms for the computation of the Walsh, Reed-Muller, arithmetic and...

In VLSI CAD, difficult optimization problems have to be solved on a constant basis. Various optimization techniques have been proposed in the past. While some of these methods have been shown to work well in applications and have become somewhat established over the years, other techniques have been ignored.
Recently, there has been a growing interest in optimization algorithms based on principles observed in nature, termed Evolutionary Algorithms (EAs).
Evolutionary Algorithms in VLSI CAD presents the basic concepts of EAs, and considers the application of EAs in VLSI...

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...

The design process of digital circuits is often carried out in individual steps, like logic synthesis, mapping, and routing. Since originally the complete process was too complex, it has been split up in several - more or less independen- phases. In the last 40 years powerful algorithms have been developed to find optimal solutions for each of these steps. However, the interaction of these different algorithms has not been considered for a long time. This leads to quality loss e. g. in cases where highly optimized netlists fit badly onto the target architecture. Since the resulting circuits...

Modern circuits may contain up to several hundred million transistors. In the meantime it has been observed that verification becomes the major bottleneck in design flows, i.e. up to 80% of the overall design costs are due to verification. This is one of the reasons why several methods have been proposed as alternatives to classical simulation. Simulation alone cannot guarantee sufficient coverage of the design resulting in bugs that may remain undetected.
As alternatives formal verification techniques have been proposed. Instead of simulating a design the correctness is proven by formal...

The size of technically producible integrated circuits increases continuously. But the ability to design and verify these circuits does not keep up with this development. Therefore, today s design ?ow has to be improved to achieve a higher productivity. In this book the current design methodology and ver- cation methodology are analyzed, a number of de?ciencies are identi?ed, and solutions are suggested. Improvements in the methodology as well as in the underlying algorithms are proposed. An in-depth presentation of preliminary concepts makes the book self-contained. Based on this foundation...

Formal verification has become one of the most important steps in circuit design. Since circuits can contain several million transistors, verification of such large designs becomes more and more difficult. Pure simulation cannot guarantee the correct behavior and exhaustive simulation is often impossible. However, many designs, like ALUs, have very regular structures that can be easily described at a higher level of abstraction. For example, describing (and verifying) an integer multiplier at the bit-level is very difficult, while the verification becomes easy when the outputs are grouped to...

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...

The development of computing machines found great success in the last decades. But the ongoing miniaturization of integrated circuits will reach its limits in the near future. Shrinking transistor sizes and power dissipation are the major barriers in the development of smaller and more powerful circuits. Reversible logic provides an alternative that may overcome many of these problems in the future. For low-power design, reversible logic offers significant advantages since zero power dissipation will only be possible if computation is reversible. Furthermore, quantum computation profits from...