On the Composition Problem for OBDDs With Multiple Variable Orders

Abstract

Ordered Binary Decision Diagram (OBDD) is a favorite data structure used for representation Boolean functions in computer-aided synthesis and verification of digital systems. The secret of its success is the efficiency of the algorithms for Boolean operations, satisfiability and equivalence check. However, the algorithms work well under condition only that the variable order of considered OBDDs is the same. In this paper, we discuss the problem of Boolean operations on OBDDs with multiple variable orders, which naturally appears, e.g., in the connection with minimization techniques based on dynamic variable reordering. Our goal is to place the problem with respect to its complexity and to point out the difficulties in finding an acceptable solution