Finding composition trees for multiple-valued functions

Abstract

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 multiple-valued functions that are fully sensitive to their variables. These functions are useful for test generation purposes, and almost all m-valued n-variable functions belong to this class as n 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.