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A Method for Approximate Equivalence Checking
 in Proceedings of the 30th IEEE International Symposium on MultipleValued Logic, Portland OR
, 2000
"... An approximate equivalence checking method is developed based on the use of partial Haar spectral diagrams (HSDs). Partial HSDs are defined and used to represent a subset of the Haar spectral coefficients for two functions. Due to the uniqueness properties of the Haar transform, a necessary conditio ..."
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An approximate equivalence checking method is developed based on the use of partial Haar spectral diagrams (HSDs). Partial HSDs are defined and used to represent a subset of the Haar spectral coefficients for two functions. Due to the uniqueness properties of the Haar transform, a necessary condition for equivalence is that the individual coefficients must have the same value. The probability that two functions are equivalent is then computed based on the number of observed, samevalued, Haar coefficients. The method described here can be useful for the case where two candidate functions require extreme amounts of computational resources for exact equivalence checking. For simplicity, the technique is explained for the binary case first and extensions to Multiple Valued Logic (MVL) are shown afterwards. Experimental results are provided to validate the effectiveness of this approach. 1. Introduction The equivalence checking problem for two logic functions of n variables, f(X) and g(Y...
Logic Circuit Equivalence Checking Using Haar Spectral Coefficients and Partial BDDs
 VLSI Design
, 2002
"... this paper. We see that given a subset of matching Haar spectral coe cients for two functions, f and g, (or alternatively, a subset of events, fS i g), the probability that f and g are indeed equivalent may be computed. By obtaining the information that a new event S i has occurred, we may update t ..."
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this paper. We see that given a subset of matching Haar spectral coe cients for two functions, f and g, (or alternatively, a subset of events, fS i g), the probability that f and g are indeed equivalent may be computed. By obtaining the information that a new event S i has occurred, we may update the value P [
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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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...
Probabilistic Equivalence Checking Using Partial Haar Spectral Diagrams
 Proc. 4th Int. Workshop Applications of the Reed–Muller Expansion in Circuit Design
, 1999
"... A probabilistic equivalence checking method is developed based on the use of partial Haar spectral diagrams (HSDs). Partial HSDs are defined and used to represent a subset of Haar spectral coefficients for two Boolean functions. The resulting coefficients are then used to compute and to iteratively ..."
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A probabilistic equivalence checking method is developed based on the use of partial Haar spectral diagrams (HSDs). Partial HSDs are defined and used to represent a subset of Haar spectral coefficients for two Boolean functions. The resulting coefficients are then used to compute and to iteratively refine the probability that two functions are equivalent. This problem has applications in both logic synthesis and verification. The method described here can be useful for the case where two candidate functions require extreme amounts of memory for a complete BDD representation. Experimental results are provided to validate the effectiveness of this approach. 1 Introduction The equivalence checking problem for two Boolean functions of n variables, f(X) and g(Y ), is addressed in this work. Here, we assume that the correspondence between the vectors of variables, X and Y is known. Although this problem is easily solved when f and g can be completely represented in BDD form, problems can ar...
Circuit design from minimized Haar wavelet series
 Proc. IEEE Int. Symp. Circuits and Systems, 35th ISCAS, Vol.3
, 2002
"... The paper discusses complexity of circuit realization through Haar wavelet series. By applying permutation of binary coordinates of indices of Haar functions, a lower complexity of circuit synthesis through higher number of zero Haar coefficients has been achieved. Experimental results confirm the m ..."
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The paper discusses complexity of circuit realization through Haar wavelet series. By applying permutation of binary coordinates of indices of Haar functions, a lower complexity of circuit synthesis through higher number of zero Haar coefficients has been achieved. Experimental results confirm the minimization of the number of nonzero Haar coefficients and the savings range from 5.25 % to 99.41 % for all benchmark functions. 1.