Synthesis of multiple sequential machines

Some further results on the synthesis of two or more sequential machines which are fed from the same input signal source are presented. It is shown that a minimal-state machine realization can always be obtained in a completely systematic way, such that the state-variable and output variable dependencies are reduced simultaneously. For two specified reduced machines, M1 and M2, with specified initial states, we find a reduced composite machine which contains both M1 and M2. The composite machine is then examined in order to determine the largest nontrivial common machine factor from which the specified outputs of of the two machines Z1 and Z2 can be generated. The techniques are applicable to the problem of realizing a machine having two or more binary output channels from the corresponding regular expressions.