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

Osnat Keren, Ilya Levin, Radomir S. Stanković

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)31-44
Number of pages14
JournalIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Issue number1
StatePublished - Jan 2011


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


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