Tandem Networks of Universal Cells

The tandem network, a row-like interconnection of cells is described. Such networks are more general than the widely studied irredundant cascade, but less general than a universal network based on, for example, the Shannon decomposition. The analysis is facilitated by the introduction of three cell-network interconnections, whose functions are characterized by certain attributes of the partition matrix of the realized function. Partition matrices have been used to significant advantage in characterizing disjunctive decompositions. They are also important in the analysis of nondisjunctive decompositions, but their application is cumbersome in such cases. It is shown that certain nondisjunctive decompositions can be handled easily as operations on partition matrices. A counting technique is developed which shows that the number of functions realized by tandem networks is significantly larger than that realized by cascades. In addition, a synthesis technique is shown for constructing a tandem network to realize a given function.