Determining the number of paths in decision diagrams by using autocorrelation coefficients

Osnat Keren; Ilya Levin; Radomir S. Stanković

doi:10.1109/tcad.2010.2069290

Determining the number of paths in decision diagrams by using autocorrelation coefficients

Osnat Keren
, Ilya Levin
, Radomir S. Stanković

Tel Aviv University
Faculty of Electronics

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

9 Scopus citations

Abstract

This paper deals with the number of paths in multiterminal binary decision diagrams (MTBDDs) and shared binary decision diagrams (SBDDs) representing a set of Boolean functions. It is shown that the number of paths in an MTBDD (SBDD) can be uniquely determined by values of specific weighted-autocorrelation coefficients. An analytical expression for the number of paths as a linear function of the values of the weighted-autocorrelation coefficients is presented. Based on this expression, a method of minimization of the number of paths is proposed. The method is based on replacing the initial set of input variables with their linear combinations. By using this method, a deterministic paths-reduction procedure, which provides MTBDDs and SBDDs with a reduced number of paths, is presented. The efficiency of the suggested approach is demonstrated on benchmark functions.

Original language	English
Pages (from-to)	31-44
Number of pages	14
Journal	IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Volume	30
Issue number	1
DOIs	https://doi.org/10.1109/tcad.2010.2069290
State	Published - Jan 2011

Keywords

Autocorrelation function
Binary decision diagram (BDD)
Linear transform
Logic synthesis
Spectral technique

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10.1109/tcad.2010.2069290

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abstract = "This paper deals with the number of paths in multiterminal binary decision diagrams (MTBDDs) and shared binary decision diagrams (SBDDs) representing a set of Boolean functions. It is shown that the number of paths in an MTBDD (SBDD) can be uniquely determined by values of specific weighted-autocorrelation coefficients. An analytical expression for the number of paths as a linear function of the values of the weighted-autocorrelation coefficients is presented. Based on this expression, a method of minimization of the number of paths is proposed. The method is based on replacing the initial set of input variables with their linear combinations. By using this method, a deterministic paths-reduction procedure, which provides MTBDDs and SBDDs with a reduced number of paths, is presented. The efficiency of the suggested approach is demonstrated on benchmark functions.",

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AB - This paper deals with the number of paths in multiterminal binary decision diagrams (MTBDDs) and shared binary decision diagrams (SBDDs) representing a set of Boolean functions. It is shown that the number of paths in an MTBDD (SBDD) can be uniquely determined by values of specific weighted-autocorrelation coefficients. An analytical expression for the number of paths as a linear function of the values of the weighted-autocorrelation coefficients is presented. Based on this expression, a method of minimization of the number of paths is proposed. The method is based on replacing the initial set of input variables with their linear combinations. By using this method, a deterministic paths-reduction procedure, which provides MTBDDs and SBDDs with a reduced number of paths, is presented. The efficiency of the suggested approach is demonstrated on benchmark functions.

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KW - Logic synthesis

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Determining the number of paths in decision diagrams by using autocorrelation coefficients

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