Identification of threshold functions and synthesis of threshold networks

Tejaswi Gowda; Sarma Vrudhula; Niranjan Kulkarni; Krzysztof Berezowski

doi:10.1109/TCAD.2010.2100232

Identification of threshold functions and synthesis of threshold networks

Tejaswi Gowda, Sarma Vrudhula, Niranjan Kulkarni, Krzysztof Berezowski

Research output: Contribution to journal › Article › peer-review

38 Scopus citations

Abstract

This paper presents a new and efficient heuristic procedure for determining whether or not a given Boolean function is a threshold function, when the Boolean function is given in the form of a decision diagram. The decision diagram based method is significantly different from earlier methods that are based on solving linear inequalities in Boolean variables that derived from truth tables. This method's success depends on the ordering of the variables in the binary decision diagram (BDD). An alternative data structure, and one that is more compact than a BDD, called a max literal factor tree (MLFT) is introduced. An MLFT is a particular type of factoring tree and was found to be more efficient than a BDD for identifying threshold functions. The threshold identification procedure is applied to the MCNC benchmark circuits to synthesize threshold gate networks.

Original language	English (US)
Article number	5752412
Pages (from-to)	665-677
Number of pages	13
Journal	IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Volume	30
Issue number	5
DOIs	https://doi.org/10.1109/TCAD.2010.2100232
State	Published - May 2011

Keywords

Binary decision diagrams
Boolean algebra
Boolean function
logic design
logic optimization
logic synthesis
threshold function
threshold logic

ASJC Scopus subject areas

Software
Computer Graphics and Computer-Aided Design
Electrical and Electronic Engineering

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10.1109/TCAD.2010.2100232

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title = "Identification of threshold functions and synthesis of threshold networks",

abstract = "This paper presents a new and efficient heuristic procedure for determining whether or not a given Boolean function is a threshold function, when the Boolean function is given in the form of a decision diagram. The decision diagram based method is significantly different from earlier methods that are based on solving linear inequalities in Boolean variables that derived from truth tables. This method's success depends on the ordering of the variables in the binary decision diagram (BDD). An alternative data structure, and one that is more compact than a BDD, called a max literal factor tree (MLFT) is introduced. An MLFT is a particular type of factoring tree and was found to be more efficient than a BDD for identifying threshold functions. The threshold identification procedure is applied to the MCNC benchmark circuits to synthesize threshold gate networks.",

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author = "Tejaswi Gowda and Sarma Vrudhula and Niranjan Kulkarni and Krzysztof Berezowski",

note = "Funding Information: Manuscript received May 4, 2010; revised August 16, 2010 and October 20, 2010; accepted November 22, 2010. Date of current version April 20, 2011. This work was supported by NSF, under Grant CCF-070283, by the Science Foundation Arizona SFAz-SBC Grant and the Stardust Foundation, and by the European Commission through FP6 Grant MOIF-CT-2006-040672. This paper was recommended by Associate Editor S. Nowick.",

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N1 - Funding Information: Manuscript received May 4, 2010; revised August 16, 2010 and October 20, 2010; accepted November 22, 2010. Date of current version April 20, 2011. This work was supported by NSF, under Grant CCF-070283, by the Science Foundation Arizona SFAz-SBC Grant and the Stardust Foundation, and by the European Commission through FP6 Grant MOIF-CT-2006-040672. This paper was recommended by Associate Editor S. Nowick.

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Identification of threshold functions and synthesis of threshold networks

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