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Determining the Number of Paths in Decision Diagrams by Using Autocorrelation Coefficients

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3 Author(s)
Keren, O. ; Sch. of Eng., Bar-Ilan Univ., Ramat-Gan, Israel ; Levin, I. ; Stankovic, R.S.

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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Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on  (Volume:30 ,  Issue: 1 )