Design of experiments in BDD variable ordering: lessons learned

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 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: statistically significant sensitivity to naming of variables; confirmation that a number of variable ordering algorithms are statistically equivalent to a random variable order assignment; and observation of a statistically anomalous variable ordering behavior of a well known benchmark circuit isomorphic class when analyzed under 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.