TY - JOUR
T1 - Determining the number of paths in decision diagrams by using autocorrelation coefficients
AU - Keren, Osnat
AU - Levin, Ilya
AU - Stanković, Radomir S.
PY - 2011/1
Y1 - 2011/1
N2 - 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.
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.
KW - Autocorrelation function
KW - Binary decision diagram (BDD)
KW - Linear transform
KW - Logic synthesis
KW - Spectral technique
UR - http://www.scopus.com/inward/record.url?scp=84870163180&partnerID=8YFLogxK
U2 - 10.1109/tcad.2010.2069290
DO - 10.1109/tcad.2010.2069290
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AN - SCOPUS:84870163180
SN - 0278-0070
VL - 30
SP - 31
EP - 44
JO - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
JF - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IS - 1
ER -