Periodic Representations and T-Partitionable Equivalents of Sequential Machines

This paper deals with the problem of finding nontrivial periodic representations, with not necessarily null transient duration, of deterministic sequential machines. The well-known results in this area, based on means of d-equivalence partitions or regular d-partitions on the set of internal states of a sequential machine A, are generalized. Apart from this, the problem of finding nontrivial periodic representations of A is solved here by the well-known methods of input-independent partitions on the set of internal states of A and by the operation of the (τ, T) numeration introduced here.