Bound-set preserving ROBDD variable orderings may not be optimum

This paper reports a result concerning the relation between the best variable orderings of an ROBDD G_f and the decomposition structure of the Boolean function f represented by G_f. It was stated in [S.-W. Jeong (1992)] that, if f has a decomposition of type f(X)-g(h₁(Y₁),h₂(Y₂),...h_k(Y_k)), where {Y₁}, i∈{1,2,...,k}, is a partition of X, then one of the orderings which keeps the variables within the sets {Y₁} adjacent is a best ordering for G_f. Using a counterexample, we show that this statement is incorrect.