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Logic Circuit Equivalence Checking Using Haar Spectral Coefficients and Partial BDDs
 VLSI DESIGN
, 2002
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A method for approximate equivalence checking
 in Proceedings of the 30th IEEE International Symposium on MultipleValued Logic, Portland OR
, 2000
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Circuit design from minimized Haar wavelet series
 Proc. IEEE Int. Symp. Circuits and Systems, 35th ISCAS, Vol.3
, 2002
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Applications of Circuit Probability Computation Using Decision Diagrams
 IN PROCEEDINGS 1997 IEEE PACIFIC RIM CONFERENCE ON COMMUNICATIONS, COMPUTERS AND SIGNAL PROCESSING
, 1997
"... Digital circuit output probabilities provide meaningful information regarding the behavior of combinational logic circuits. The computation of the probability values can be computationally expensive when Boolean equations or netlists are used. When the circuits are represented by compact decision di ..."
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Digital circuit output probabilities provide meaningful information regarding the behavior of combinational logic circuits. The computation of the probability values can be computationally expensive when Boolean equations or netlists are used. When the circuits are represented by compact decision diagrams (DD), efficient algorithms exist for determining the probability values. The use of the probabilities based on decision diagram representations are examined here. Specifically, research results of investigations into spectra computation, synthesis, symmetry detection and DD reordering are surveyed.
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...
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...
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"... ACKNOWLEDGEMENTS I would like to think my thesis advisor, Dr. Thornton, for the opportunity to work on this project, for his many insights into this research, and for the numerous times that he reviewed my thesis. I would also like to think Dr. Andrews and Dr. Lacy for serving on ..."
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ACKNOWLEDGEMENTS I would like to think my thesis advisor, Dr. Thornton, for the opportunity to work on this project, for his many insights into this research, and for the numerous times that he reviewed my thesis. I would also like to think Dr. Andrews and Dr. Lacy for serving on
Logic Circuit Equivalence Checking Using Haar Spectral
"... 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.
Generalized Haar Spectral Representations and Their Applications
"... Haar transform is known to have the smallest computational requirement and has been used mainly for pattern recognition and image processing. Although the properties of Haar spectra of Boolean functions have considerable interest and attraction, the majority of publications to date have employed the ..."
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Haar transform is known to have the smallest computational requirement and has been used mainly for pattern recognition and image processing. Although the properties of Haar spectra of Boolean functions have considerable interest and attraction, the majority of publications to date have employed the Walsh rather than Haar transform in their considerations. It is mainly due to the fact that up to recently there was no efficient method of calculating Haar spectra directly from reduced representations of Boolean functions such as decision diagrams and cubes. Recently, efficient methods based on Decision Diagrams and cubical representation for the computation of Haar spectra have been developed. Two methods based on decision diagrams and a new data structure called the "Haar Spectral Diagram" is discussed. The method to calculate Haar spectra from disjoint cubes of Boolean functions is also presented. A concept of paired Haar transform for representation and efficient optimization of systems of incompletely specified Boolean functions will be discussed. Finally another form of Haar transform, so called "Sign Haar Transform" is discussed and basic properties of Boolean functions in its spectral domain are shown. Various applications of Haar transform in logic design are also mentioned.
Reprints available directly from the publisher Published by license under the OCP Science imprint, Photocopying permitted by license only a member of the Old City Publishing Group Properties of Logic Functions in Spectral Domain of Sign HadamardHaar Tran
"... (Recommended for publication by Radomir S. Stankovic) ..."