Asymptotically Optimal Bounds for OBDDs and the Solution of Some Basic OBDD Problems

摘要

Ordered binary decision diagrams (OBDDs) are nowadays the most common dynamic data structure or representation type for Boolean functions. Among the many areas of application are verification, model checking, and computer aided design. For many functions it is easy to estimate the OBDD size but asymptotically optimal bounds are only known in simple situations. In this paper, methods for proving asymptotically optimal bounds are presented and applied to the solution of some basic problems concerning OBDDs. The largest size increase by a synthesis step of π-OBDDs followed by an optimal reordering is determined as well as the largest ratio of the size of deterministic finite automata, quasi-reduced OBDDs, and zero-suppressed BDDs compared to the size of OBDDs. Moreover, the worst case OBDD size of functions with a given number of 1-inputs is investigated.