Minimization of ordered pseudo Kronecker decision diagrams

Abstract

The introduction of Decision Diagrams (DDs) has brought new means towards solving many of the problems involved in digital circuit design. Compactness of the representation is one key issue. Ordered Pseudo Kronecker Decision Diagrams (OPKDDs) together with the use of complemented edges is known to offer the most general ordered read-once DD representation at the bit-level, hence OPKDDs hold all minimal sized bit-level ordered DDs for a given function. This representation allows us to trade-off diagram canonicity against compactness. Ternary-OPKDDs (TOPKDDs) implicitly holds all OPKDDs for a given variable order. We state the canonicity criteria for TOPKDDs having complemented edges and develop an efficient sifting based method for their minimization. Furthermore, a heuristic minimization algorithm for OPKDDs is devised, utilizing the redundancies of Ternary-OPKDDs (TOPKDDs). Experiments on a set of MCNC benchmarks confirm the potential compactness of OPKDDs and demonstrate the efficiency of the proposed heuristics.