Decision diagram based techniques for the Haar wavelet transform

Hansen, Jeffery P.; Sekine, Masatoshi

doi:10.1109/icics.1997.647057

Cited by 23 publications

(25 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Figure 4 is similar to the diagram originally appearing in Ref. [9] and illustrates this relationship.…”

Section: Haar Spectral Diagramssupporting

confidence: 50%

“…The Haar spectral coefficients may be obtained through the use of any efficient method such as those in Refs. [8,9,18]. We note that given the i-th Haar spectral coefficient for a function, f, and a function, g, there appear to be four possibilities as given in Table III.…”

Section: Relation Of Haar Coefficients To Probabilistic Eventsmentioning

confidence: 99%

“…[9], a directed graph referred to as a Haar Spectral Diagram (HSD) is defined that represents the Haar spectrum of a Boolean function. HSDs are isomorphic to BDDs (with the exception that all BDD terminal vertices are "mapped" to a common HSD terminal vertex).…”

Section: Haar Spectral Diagramsmentioning

confidence: 99%

“…[9] that allows the Haar spectral coefficients to be represented as a HSD with the concept of the partial BDD as given in [16]. This allows for a partial function representation to be used for quickly computing subsets of Haar spectral coefficients avoiding problems that may arise for functions that result in very large BDDs when represented in their fully specified form.…”

Section: Introductionmentioning

confidence: 99%

“…Given a set of Haar spectral coefficients, we examine the probability that f ðXÞ ¼ gðYÞ: This allows the equivalence checking problem to be iteratively refined in terms of possible error by accounting for the existence of more matching coefficients. Thus, techniques that provide subsets of Haar spectral coefficients [8,9,18] for representations of f and g can be used for non-tautology checking. A similar approach using an arithmetic transform and a decision diagram structure known as an Interleaved BDD (IBDD) has also been proposed [12].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Logic Circuit Equivalence Checking Using Haar Spectral Coefficients and Partial BDDs

2000

View full text Add to dashboard Cite

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.

show abstract

“…Figure 4 is similar to the diagram originally appearing in Ref. [9] and illustrates this relationship.…”

Section: Haar Spectral Diagramssupporting

confidence: 50%

Section: Relation Of Haar Coefficients To Probabilistic Eventsmentioning

confidence: 99%

Section: Haar Spectral Diagramsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Logic Circuit Equivalence Checking Using Haar Spectral Coefficients and Partial BDDs

2000

View full text Add to dashboard Cite

show abstract

Logic Functions

2007

Spectral Logic and Its Applications for the Design of Digital Devices

View full text Add to dashboard Cite

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor the author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993, or fax (317) 572-4002.Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our Web site at www.wiley.com.

show abstract