Minimization of binary decision diagrams based on exchanges of variables

The authors present a novel exact algorithm and gradual improvement methods for minimizing binary decision diagrams (BDDs). In the exact minimization algorithm, the optimum order is searched by the exchanges of variables of BDDs based on the framework of the algorithm of S.J. Friedman and K.J. Supowit (1990). The use of the BDD representation of a given function and intermediate functions makes it possible to produce pruning into the method, which drastically reduces the computation cost. The authors succeeded in minimizing a 17-variable function by the use of the BDD representation of intermediate functions and the introduction of pruning. They also propose a greedy method and a simulated annealing method based on exchanges of two arbitrary variables, and a greedy method based on exchanges of adjacent m variables for m=3 and 4.<>