Design of Experiments in BDD Variable Ordering

Design of Experiments in BDD Variable Ordering: Lessons Learned Justin E. Harlow III1 Franc Brglez2 1Dept. of Electrical & Computer Engineering, Duke University, Durham, NC 27708 2CBL (Collaborative Benchmarking Lab), Dept. of Comp. Science, Box 7550, NC State U., Raleigh, NC 27695 http://www.cbl.ncsu.edu/ 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 f1, 2, ...g-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 signi cant sensitivity to naming of variables, (2) con rmation 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 wellknown benchmark circuit isomorphic class when analyzed under a single and multiple outputs. On the positive side, the methodology supports a statistically signi cant merit evaluation of any newly introduced variable ordering algorithm, including the one brie y introduced in this paper.