Trinity Algebra and its Application to Machine Decompositions

Abstract In this paper a concept of partition trinity is introduced and its general properties, as an algebraic system, are investigated. Partition trinity and trinity algebra efficiently give the information dependence between inputs, states, and outputs within a triple of partitions, and they serve as a powerful tool to the full-decompositions of machines. The decomposition is especially significant in the case of decompositions associated with the pins of VLSI devices.