Design of experiments in BDD variable ordering: Lessons learned

Abstract

Applying the Design of Experiments methodology to the evaluation of BDD variable ordering algorithms has yielded a number of conclusive results. The methodology relies on the recently introduced equivalence classes of functionally perturbed circuits that maintain logic invariance, or are within {1, 2, ...}-minterms of the original reference circuit function, also maintaining entropy-invariance. For some of the current variable ordering algorithms and tools, the negative results include: (1) statistically significant sensitivity to naming of variables, (2) confirmation that a number of variable ordering algorithms are statistically equivalent to a random variable order assignment, and (3) observation of a statistically anomalous variable ordering behavior of a well-known benchmark circuit isomorphic class when analyzed under a single and multiple outputs. On the positive side, the methodology supports a statistically significant merit evaluation of any newly introduced variable ordering algorithm, including the one briefly introduced in this paper.