A simple implementation of determinant decision diagram

Determinant decision diagram (DDD) uses a Binary Decision Diagram (BDD) to represent the Laplace expansion of a determinant. It is used as the core computation engine in some modern symbolic circuit simulators. The traditional implementations rely on a BDD package for the common-data sharing operations in which symbol ordering plays an essential role. This paper proposes a simple implementation method which does not use any BDD package. Sharing is implemented by directly hashing minors, while the requirement on symbol ordering is weakened to an expansion ordering. The basic mechanism used is a natural formulation of layered expansion which is analogous to manual expansion of a determinant, hence it is easily understood. The simplified DDD construction method not only makes the DDD implementation straightforward, but also results in greater efficiency. A simulator developed based on this new method solves the μa725 op-amp circuit in a few seconds by flat expansion.