Reduction of average path length in binary decision diagrams by spectral methods

This paper deals with static techniques for reducing the Average Path Length (APL) of binary decision diagrams. The APL is proved to be a linear function of a folded autocorrelation function values. It is well known that the APL is sensitive to the reordering of the input variables, the explicit expression of the APL determines an optimal ordering criterion based on the function properties. Moreover, the APL can be further reduced by using linear functions of the input variables. Two linearization procedures for the linearization are presented: a) a minimization procedure using the autocorrelation values (time domain) and b) a minimization algorithm based on the mutual information between the Boolean function and a linear function of the input variables (Walsh spectrum). The time-domain approach outperforms the established information-theory approach. Experimental results show the efficiency of the suggested techniques.