Blockwise Variable Orderings for Shared BDDs

In this paper we consider the problem of characterizing optimal variable orderings for shared OBDDs of two Boolean functions fi = gi i hi, i = 1, 2, where i is an operator from the Base B 2 and gi (resp. hi) depends only on x-variables (resp. y-variables). Tree-like circuits provide an example for such functions. In the special case f1 = f2, Sauerhoff, Wegener and Werchner [6] proved that there is some optimal ordering where all x-variables are tested before all y-variables or vice versa. We show that this is also true for arbitrary f1, f2 provided that 1 = and 2 = , and for shared OBDDs with complemented edges and arbitrary f1, f2 provided that 1 = and 2 = . For all other combinations of 1 und 2 we give counterexamples.

• Type: Conference
• Year: 1998
• Where: MFCS
• Authors: Harry Preuß, Anand Srivastav
• Keywords: Boolean Functions, MFCS 1998, Optimal Variable Orderings, Theoretical Computer Science, Tree-like Circuits