Restricted simple disjunctive decompositions based on grouping symmetric variables

This paper presents an efficient method for a simple disjunctive decomposition, where candidates for the bound set are restricted to sets of symmetric variables to reduce the computation cost. Symmetric variables are detected by depth-first traversals of an ordered binary decision diagram (OBDD), and decompositions are carried out by changing the variable order of the OBDD. We do not change the variable order until the change is really needed. Experimental results show that even if the decomposition form was restricted, many practical functions could be decomposed. The execution time for decomposition was very small even for functions with many variables. Combined with an exhaustive search, the method successfully decomposed some functions that could not be decomposed by exhaustive search alone in a practical amount of time.