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Functional Decomposition with Applications to FPGA Synthesis - Christoph Scholl

Functional Decomposition with Applications to FPGA Synthesis

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Published: 31st October 2001
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During the last few years Field Programmable Gate Arrays (FPGAs) have become increasingly important. Thanks to recent breakthroughs in technology, FPGAs offer millions of system gates at low cost and considerable speed. Functional decomposition has emerged as an essential technique in automatic logic synthesis for FPGAs. Functional decomposition as a technique to find realizations for Boolean functions was already introduced in the late fifties and early sixties by Ashenhurst, Curtis, Roth and Karp. In recent years, however, it has attracted a great deal of renewed attention, for several reasons. First, it is especially well suited for the synthesis of lookup-table based FPGAs. Also, the increased capacities of today's computers as well as the development of new methods have made the method applicable to larger-scale problems. Modern techniques for functional decomposition profit from the success of Reduced Ordered Binary Decision Diagrams (ROBDDs), data structures that provide compact representations for many Boolean functions occurring in practical applications. We have now seen the development of algorithms for functional decomposition which work directly based on ROBDDs, so that the decomposition algorithm works based on compact representations and not on function tables or decomposition matrices as in previous approaches. The book presents, in a consistent manner, a comprehensive presentation of a multitude of results stemming from the author's as well as various researchers' work in the field. Apart from the basic method, it also covers functional decomposition for incompletely specified functions, decomposition for multi-output functions and non-disjoint decomposition. Functional Decomposition with Application to FPGA Synthesis will be of interest both to researchers and advanced students in logic synthesis, VLSI CAD, and Design Automation as well as professionals working in FPGA design and the development of algorithms for FPGA synthesis.

'It is an excellent book. I suppose that it is of interest to researchers, advanced students, and professionals working in electronic design automation.' Zentral Blatt Mathematik, 989 (2002)

Preface
Acknowledgments
Introduction
Realizations of Boolean Functionsp. 1
Circuitsp. 3
Boolean Expressionsp. 8
Binary Decision Diagrams (BDDs)p. 10
Field Programmable Gate Arrays (FPGAs)p. 16
Complexity of realizations of Boolean functionsp. 20
Minimization of BDDsp. 23
BDD minimization for completely specified functionsp. 23
BDD minimization for incompletely specified functionsp. 38
Functional Decomposition for Completely Specified Single-Output Functionsp. 69
Definitionsp. 70
Decomposition and Field Programmable Gate Arraysp. 73
Minimizing the number of decomposition functionsp. 74
Nontrivial decomposability - theoretical considerationsp. 81
Examples of circuits derived by decompositionp. 88
Decomposition and ROBDD representationsp. 91
Variable partitioningp. 101
The encoding problemp. 107
Functional Decomposition for Completely Specified Multi-Output Functionsp. 123
A motivating examplep. 124
Output partitioning and input partitioningp. 129
Computation of common decomposition functionsp. 134
Experimentsp. 162
Alternative methodsp. 166
Functional Decomposition for Incompletely Specified Functionsp. 177
Decomposition and BDD minimization for incompletely specified functionsp. 178
One-sided decomposition of incompletely specified functionsp. 178
Two-sided decomposition of incompletely specified functionsp. 180
Computation of incompletely specified decomposition and composition functionsp. 181
Multi-output functionsp. 185
Experimental resultsp. 194
Non-Disjoint Decompositionsp. 201
Motivationp. 202
Integration of non-disjoint into disjoint decompositionp. 205
Computing non-disjoint variable sets for decompositionp. 208
Large Circuitsp. 213
Appendicesp. 219
An example for an FPGA devicep. 219
Complexity of CMp. 223
Characterization of weak and strong symmetryp. 225
Complexity of MSPp. 227
Making a function strongly symmetricp. 229
Compatibility of don't care minimization methodsp. 233
Symmetries and decomposabilityp. 235
Complexity of CDFp. 239
ROBDD based computation of compatibility classesp. 245
Maximal don't care setsp. 249
Indexp. 261
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792375852
ISBN-10: 0792375858
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 264
Published: 31st October 2001
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.4 x 15.6  x 2.54
Weight (kg): 0.57