On an optimization technique using Binary Decision Diagram

TL;DR

This paper introduces a BDD-based method for two-level logic minimization that is significantly faster than previous techniques, especially for large circuits, though its effectiveness depends on variable ordering.

Contribution

The paper presents a novel BDD-based approach for minimizing Boolean functions using disjoint sum of products, improving speed and handling larger circuits than prior methods.

Findings

The BDD-based method is orders of magnitude faster than enumerative techniques.

Resulting DSOPs are comparable or better in size than existing methods.

The approach enables handling of larger circuit instances previously infeasible.

Abstract

Two-level logic minimization is a central problem in logic synthesis, and has applications in reliability analysis and automated reasoning. This paper represents a method of minimizing Boolean sum of products function with binary decision diagram and with disjoint sum of product minimization. Due to the symbolic representation of cubes for large problem instances, the method is orders of magnitude faster than previous enumerative techniques. But the quality of the approach largely depends on the variable ordering of the underlying BDD. The application of Binary Decision Diagrams (BDDs) as an efficient approach for the minimization of Disjoint Sums-of-Products (DSOPs). DSOPs are a starting point for several applications. The use of BDDs has the advantage of an implicit representation of terms. Due to this scheme the algorithm is faster than techniques working on explicit representations and the application to large circuits that could not be handled so far becomes possible. Theoretical studies on the influence of the BDDs to the search space are carried out. In experiments the proposed technique is compared to others. The results with respect to the size of the resulting DSOP are as good or better as those of the other techniques.