Binary decision diagrams and their applications to implicit enumeration techniques in logic synthesis
A Comment on 'Graph-Based Algorithm for Boolean Function Manipulation'
IEEE Transactions on Computers
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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 [1] that, if f has a decomposition of type f(X) = g(h_1(Y_1), h_2(Y_2), \ldots, h_k(Y_k)), where \{Y_i\}, i \in \{1,2,\ldots,k\}, is a partition of X, then one of the orderings which keeps the variables within the sets \{Y_i\} adjacent is a best ordering for G_f. Using a counterexample, we show that this statement is incorrect.