Finding Composition Trees for Multiple-Valued Functions

The composition tree of a given function, when it exists, provides a representation of the function revealing all possible disjunctive decompositions, thereby suggesting a realization of the function at a minimal cost. Previously and independently, the authors had studied the class of multiplevalued functions that are fully sensitive to their variables. These functions are useful for test generation purposes, and almost all -valued -variable functions belong to this class as increases. All functions in this class have composition trees. This paper presents a recursive algorithm for generating the composition tree for any function in this class. The construction proceeds top-down and makes immediate use of any encountered decomposition, which reduces the (in general exponential) computation time.