The influence of the number of values in sub-functions on the effectiveness and efficiency of the functional decomposition

General functional decomposition has important applications in many fields of modern engineering and science. However, its practical usefulness for very complex systems is limited by the lack of an effective and efficient method for the construction of high quality sub-systems. One of the three basic problems of sub-system construction is the choice of an appropriate multi-valued sub-function to be computed by a certain sub-system. In this paper we show that the number of values of the sub-function is the decisive factor in sub-function selection. It shows a very strong positive correlation with both the number of logic blocks and the number of logic levels in the decomposition network, i.e. with the cost and delay of the network. This is a very important result from the practical viewpoint, because its exploitation enables efficient construction of high-quality multi-level circuits, by selection of a sub-function with the minimum possible number of values at each decomposition step. This result also gives a link for the input support selection for sub-systems. The selected input support should enable construction of a sub-function with the minimum possible number of values.