The full decomposition of sequential machines with the state and output behaviour realization

The design of large logic systems leads to the practical problem how to decompose a complex system into a number of simpler subsystems. The decomposition theory of sequential machines tries to find answers to this problem for sequential machines. For many years, the "simpler" machine was defined as a machine with fewer states and, therefore, state-decompositions of sequential machines were considered. Together with the progress in LSI
technology and the introduction of array logic into the design of
sequential circuits a real need arose for decompositions not only
on states of sequential machines but on inputs and outputs too,
i.e. for full-decompositions. In this report, a general and unified classification of fulldecompositions is presented, formal definitions of different sorts of full-decompositions for Mealy and Moore machines are
introduced and theorems about the existence of fulldecompositions with the state and output behaviour realization are formulated and proved. The presented theorems have a straightforward practical interpretation. Based on them, a set of algorithms has been developed and a system of programs has been made for computing the different sorts of decompositions.