History-Based Dynamic Minimization During BDD Construction

Abstract

Binary Decision Diagrams (BDDs) are the state-of-the-art data structure in VLSI CAD. Since their size largely depends on the chosen variable ordering, dynamic variable reordering methods, like sifting, often have to be applied while the BDD for a given circuit is constructed. Usually sifting is called each time a given node limit is reached and it is therefore called frequently during the construction of large BDDs. Often most of the runtime is spent for sifting while the BDD is built. In this paper we propose an approach to reduce runtime (and space requirement) during BDD construction by using history-based decision procedures. Dependent on the history of the construction process different types of sifting are called. We propose two methods that consider the quality of the hash table and the size reduction of previous sifting runs, respectively. Experimental results show that both approaches reduce the runtime significantly, i.e. by more than 40% on average.

Polynomial Circuit Verification using BDDs

“…Even in cases where the final result can efficiently be represented, intermediate results might be too large to be handled. This has already been observed in early applications of BDDs and as a consequence approaches have been presented to reduce the peak size during the construction [16,14,11]. These techniques were either heuristic in nature or had prohibitive large run times.…”