From the Publisher:
Switching Theory for Logic Synthesis covers the basic topics of switching theory and logic synthesis in fourteen chapters. Chapters 1 through 5 provide the mathematical foundation. Chapters 6 through 8 include an introduction to sequential circuits, optimization of sequential machines and asynchronous sequential circuits. Chapters 9 through 14 are the main feature of the book. These chapters introduce and explain various topics that make up the subject of logic synthesis: multi-valued input two-valued output function, logic design for PLDs/FPGAs, EXOR-based design, and complexity theories of logic networks.
An appendix providing a history of switching theory is included. The reference list consists of over four hundred entries.
Switching Theory for Logic Synthesis is based on the author's lectures at Kyushu Institute of Technology as well as seminars for CAD engineers from various Japanese technology companies.
Switching Theory for Logic Synthesis will be of interest to CAD professionals and students at the advanced level. It is also useful as a textbook, as each chapter contains examples, illustrations, and exercises.

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Switching Theory for Logic Synthesis

Ordered Binary Decision Diagrams (OBDDs) have found widespread use in CAD applications such as formal verification, logic synthesis, and test generation. OBDDs represent Boolean functions in a form that is both canonical and compact for many practical cases. They can be generated and manipulated by efficient graph algorithms. Researchers have found that many tasks can be expressed as series of operations on Boolean functions, making them candidates for OBDD-based methods. The success of OBDDs has inspired efforts to improve their efficiency and to expand their range of applicability. Techniques have been discovered to make the representation more compact and to represent other classes of functions. This has led to improved performance on existing OBDD applications, as well as enabled new classes of problems to be solved. This paper provides an overview of the state of the art in graph-based function representations. We focus on several recent advances of particular importance for formal verification and other CAD applications.

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Binary decision diagrams and beyond: enabling technologies for formal verification

This paper describes a novel logic decomposition theory and a practical logic synthesis system, BDS. It is based on a new binary decision diagrams (BDD) decomposition technique which supports all types of decomposition structures, including AND, OR, XOR, and complex MUX, both algebraic and Boolean. As a result, the method is very efficient in synthesizing both AND/OR and XOR-intensive functions. It also has a capability to handle very large circuits, as it employs the BDD decomposition in the partitioned Boolean network environment. The experimental results show that BDD-based logic decomposition is a promising alternative to the existing logic optimization approaches. In particular, it offers a superior runtime advantage over traditional logic synthesis systems.

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BDS: a BDD-based logic optimization system

Regarding finite state machines as Markov chains facilitates the application of probabilistic methods to very large logic synthesis and formal verification problems. In this paper we present symbolic algorithms to compute the steady-state probabilities for very large finite state machines (up to 10/sup 27/ states). These algorithms, based on Algebraic Decision Diagrams (ADD's)-an extension of BDD's that allows arbitrary values to be associated with the terminal nodes of the diagrams-determine the steady-state probabilities by regarding finite state machines as homogeneous, discrete-parameter Markov chains with finite state spaces, and by solving the corresponding Chapman-Kolmogorov equations. We first consider finite state machines with state graphs composed of a single terminal strongly connected component; for this type of system we have implemented two solution techniques: One is based on the Gauss-Jacobi iteration, the other one is based on simple matrix multiplication. Then we extend our treatment to the most general case of systems which can be modelled as finite state machines with arbitrary transition structures; here our approach exploits structural information to decompose and simplify the state graph of the machine. We report experimental results obtained for problems on which traditional methods fail.

Markovian analysis of large finite state machines

Decision diagrams (DDs) are the state-of-the-art data structure in VLSI CAD and have been successfully applied in many other fields. DDs are widely used and are also integrated in commercial tools. This special section comprises six contributed articles on various aspects of the theory and application of DDs. As preparation for these contributions, the present article reviews the basic definitions of binary decision diagrams (BDDs). We provide a brief overview and study theoretical and practical aspects. Basic properties of BDDs are discussed and manipulation algorithms are described. Extensions of BDDs are investigated and by this we give a deeper insight into the basic data structure. Finally we outline several applications of BDDs and their extensions and suggest a number of articles and books for those who wish to pursue the topic in more depth.

Binary decision diagrams in theory and practice

Edge-Valued Binary-Decision Diagrams (EVBDD's) are directed acyclic graphs that can represent and manipulate integer functions as effectively as Ordered Binary-Decision Diagrams OBDD's) do for Boolean functions. They have been used in logic verification for showing the equivalence between Boolean functions and arithmetic functions. In this paper, we present EVBDD-based algorithms for solving integer linear programs, computing spectral coefficients of Boolean functions, and performing function decomposition. These algorithms have been implemented in C under the SIS environment and experimental results are provided. >

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M. Pedram

Papers

EVBDD-based algorithms for integer linear programming, spectral transformation, and function decomposition