In this paper, the system full-decomposition theory is introduced and its mathematical properties, as an algebraic system, are provided. A partition trinity of the algebra on a machine gives efficiently 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. In information processing system, the full-decomposition is especially significant in the case of decompositions related to the pins of VLSI devices.
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