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22
Low Power CMOS Digital Design
 IEEE Journal of Solid State Circuits
, 1995
"... : Motivated by emerging battery operated applications that demand intensive computation in portable environments, techniques are investigated which reduce power consumption in CMOS digital circuits while maintaining computational throughput. Techniques for low power operation are shown which use the ..."
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Cited by 102 (0 self)
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: Motivated by emerging battery operated applications that demand intensive computation in portable environments, techniques are investigated which reduce power consumption in CMOS digital circuits while maintaining computational throughput. Techniques for low power operation are shown which use the lowest possible supply voltage coupled with architectural, logic style, circuit and technology optimizations. An architectural based scaling strategy is presented which indicates that the optimum voltage is much lower than that determined by other scaling considerations. This optimum is achieved by trading increased silicon area for reduced power consumption. 1.0 Introduction With much of research efforts of the past ten years directed toward increasing the speed of digital systems, presentday technologies possess computing capabilities which make possible powerful personal workstations, sophisticated computer graphics, and multimedia capabilities such as realtime speech recognition and...
Efficient Calculation of Spectral Coefficients and Their Applications
 IEEE Trans. on CAD/ICAS
, 1995
"... Spectral methods for analysis and design of digital logic circuits have been proposed and developed for several years. The widespread use of these techniques has suffered due to the associated computational complexity. This paper presents a new approach for the computation of spectral coefficient ..."
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Cited by 21 (6 self)
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Spectral methods for analysis and design of digital logic circuits have been proposed and developed for several years. The widespread use of these techniques has suffered due to the associated computational complexity. This paper presents a new approach for the computation of spectral coefficients with polynomial complexity. Usually, the computation of the spectral coefficients involves the evaluation of inner products of vectors of exponential length. In the new approach, it is not necessary to compute inner products, rather, each spectral coefficient is expressed in terms of a measure of correlation between two Boolean functions. This formulation coupled with compact BDD representations of the functions reduces the overall complexity. Further, some computer aided design applications are presented that can make use of the new spectrum evaluation approach. In particular, the basis for a synthesis method that allows spectral coefficients to be computed in an iterative manner ...
Ternary Decision Diagrams Survey
 Proc. ISMVL '97
, 1997
"... This paper surveys seven types of TDDs: General TDD, SOP TDD, ESOP TDD, AND TDD, prime TDD, EXOR TDD, and Kleene TDD. We give new definitions for SOP TDDs and ESOP TDDs and introduce unifying terminology. After showing some theoremsoncomplexities, we compare the sizes of these TDDs using benchmark f ..."
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Cited by 10 (2 self)
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This paper surveys seven types of TDDs: General TDD, SOP TDD, ESOP TDD, AND TDD, prime TDD, EXOR TDD, and Kleene TDD. We give new definitions for SOP TDDs and ESOP TDDs and introduce unifying terminology. After showing some theoremsoncomplexities, we compare the sizes of these TDDs using benchmark functions. Finally, we review important works on TDDs.
A Numerical Method for ReedMuller Circuit Synthesis
 Proceedings of the IFIP WG 10.5 Workshop on Applications of the ReedMuller Expansion in Circuit Design
, 1993
"... A numerical computation based circuit synthesis technique is presented for the ReedMuller canonical form. The synthesis methodology is reduced to the problem of finding a solution to linear system of equations in the realfield. The mathematical formulation for this technique is developed and it is ..."
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Cited by 5 (5 self)
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A numerical computation based circuit synthesis technique is presented for the ReedMuller canonical form. The synthesis methodology is reduced to the problem of finding a solution to linear system of equations in the realfield. The mathematical formulation for this technique is developed and it is shown that a unique solution exists. A synthesis example is presented along with a discussion on implementation issues. 1 Introduction As the complexity of VLSI circuitry increases, testability concerns tend to grow proportionally. The wellknown properties of the ReedMuller canonical form make it an attractive candidate for testable circuit implementations [1]. Previously, the automated synthesis of ReedMuller logic circuits was accomplished via symbolic Boolean algebra manipulations [2] [3], or the use of the ReedMuller transforms [9] [10] [13]. In this paper, we present an approach similar to the ReedMuller transform technique, however, we develop a more general mathematical framewo...
GRMIN: A Heuristic Simplification Algorithm for Generalized ReedMuller Expressions
, 1995
"... A generalized ReedMuller expression (GRM) is a type of ANDEXOR expressions. In a GRM, each variable may appear both complemented and uncomplemented. Networks realized using GRMs are easily tested. This paper presents GRMIN, a heuristic simplification algorithm for GRMs of multipleoutput functi ..."
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Cited by 4 (1 self)
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A generalized ReedMuller expression (GRM) is a type of ANDEXOR expressions. In a GRM, each variable may appear both complemented and uncomplemented. Networks realized using GRMs are easily tested. This paper presents GRMIN, a heuristic simplification algorithm for GRMs of multipleoutput functions. GRMIN uses eight rules. As the primary objective, it reduces the number of products, and as the secondary objective, it reduces the number of literals. Experimental results show that, in most cases, GRMs require fewer products than conventional sumofproducts expressions (SOPs). GRMIN outperforms existing algorithms.
Efficient Spectral Coefficient Calculation Using Circuit Output Probabilities
 Digital Signal Processing: A Review Journal
, 1994
"... Many problems in the field of digital logic may be solved more efficiently in the spectral domain than in the Boolean domain. However, the primary drawback of spectral techniques is the large complexity associated with the calculation of the spectrum of a Boolean function. We present a new method ..."
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Cited by 3 (3 self)
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Many problems in the field of digital logic may be solved more efficiently in the spectral domain than in the Boolean domain. However, the primary drawback of spectral techniques is the large complexity associated with the calculation of the spectrum of a Boolean function. We present a new method for the computation of a spectral coefficient that has a complexity equal to O(j E j) where j E j is the number of edges in a binary decision diagram characterizing the circuit. This result is especially significant for techniques that require the calculation of only a few spectral coefficients since it allows the computations to be accomplished very efficiently and does not require storage resources for a large number values. Furthermore, this method holds for any general spectral transform and does not require the transformation matrix to be recursively defined or sparse. 1 Introduction There have been many applications proposed and developed using spectral methods for logic c...
Applications and Efficient Computation of Spectral Coefficients for Digital Logic
, 1994
"... Spectral methods for analysis and design of digital logic circuits have been proposed and developed for several years. The widespread use of these techniques has suffered due to the associated computational complexity. This paper presents a new approach for the computation of spectral coefficient ..."
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Cited by 2 (2 self)
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Spectral methods for analysis and design of digital logic circuits have been proposed and developed for several years. The widespread use of these techniques has suffered due to the associated computational complexity. This paper presents a new approach for the computation of spectral coefficients with polynomial complexity. Usually, the computation of the spectral coefficients involves the evaluation of inner products of vectors of exponential length. In the new approach, it is not necessary to compute inner products, rather, each spectral coefficient is expressed in terms of a measure of correlation between two Boolean functions. This formulation coupled with compact BDD representations of the functions reduces the overall complexity. Further, some computer aided design applications are presented that can make use of the new spectrum evaluation approach. In particular, a spectralbased synthesis algorithm that allows spectral coefficients to be computed in an iterative man...
BDD Based Spectral Approach for ReedMuller Circuit Realization
, 1996
"... In the past, the use of spectral coefficients for the realization of ReedMuller circuits lead to computational difficulties for functions of even moderate size due to large memory requirements. We present a new approach that overcomes these difficulties by allowing the function to be represented ..."
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Cited by 2 (1 self)
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In the past, the use of spectral coefficients for the realization of ReedMuller circuits lead to computational difficulties for functions of even moderate size due to large memory requirements. We present a new approach that overcomes these difficulties by allowing the function to be represented using a binary decision diagram thus reducing the storage requirements. In addition, the computational requirements are also reduced since an efficient method for computing the spectral coefficients is employed. Further, we illustrate the approach with examples.
Computation of Spectral Information from Logic Netlists
"... Spectral information can be used for many CAD system tasks including synthesis, verification and test vector generation. We analyze the problem of extracting spectral information from Boolean and multivalued logic netlists. It is shown that spectral information may be calculated directly from outpu ..."
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Cited by 2 (2 self)
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Spectral information can be used for many CAD system tasks including synthesis, verification and test vector generation. We analyze the problem of extracting spectral information from Boolean and multivalued logic netlists. It is shown that spectral information may be calculated directly from output probabilities and a method for extracting output probabilities from general graphs is described. As a special case, we consider AND/OR graphs which are a data structure recently proposed as an alternative to decision diagrams. Experimental results are given to demonstrate the efficiency of our approach. 1. Introduction Spectral methods have been suggested as an efficient tool for circuit design in the early 1960s. Recently, they are of growing interest, since methods have been developed that allow for efficient solutions to logic synthesis problems [15, 9]. Spectral transformations are based on a linear transformation of the entire function table in the field of integers. The truth table...
Boolean Function Representation and Spectral Characterization Using AND/OR Graphs
 INTEGRATION, The VLSI journal
, 2000
"... Methods based on AND/OR graph representations of Boolean relations provide a promising new way of approaching VLSI CAD design automation problems. AND/OR graphs can represent any Boolean network and they allow for systematic reasoning through the application of the technique of recursive learning ..."
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Cited by 1 (0 self)
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Methods based on AND/OR graph representations of Boolean relations provide a promising new way of approaching VLSI CAD design automation problems. AND/OR graphs can represent any Boolean network and they allow for systematic reasoning through the application of the technique of recursive learning. An approach to build and analyze AND/OR graphs that makes use of hashing techniques in a way similar to that for modern Decision Diagram (DD) packages is described. Additionally, the problem of extracting spectral information from AND/OR graphs is also examined. Spectral information can be used for many CAD system tasks including synthesis, verification and test vector generation. It is shown that spectral information may be calculated directly from output probabilities and a method for estimating output probabilities from AND/OR graphs is presented. Experimental results regarding the AND/OR graph package efficiency and the extraction of spectral information are provided. 1 Introdu...