 Decompositions of this kind are interesting and important for a wide variety of reasons.In general, functional decompositions are worthwhile when there is a certain "sparseness" in the dependency structure; that is, when constituent functions are found to depend on approximately disjoint sets of variables.Thus, for example, if we can obtain a decomposition of formula_11 into a hierarchical composition of functions formula_12 such that formula_13, formula_14, formula_15, as shown in the figure at right, this would probably be considered a highly valuable decomposition.