Structure of Constant Rank State Machines, and the Five Basic State Machine Types

Constant Rank (CR) state machines play an important role in the general structure theory of Finite State Machines. A machine is of constant rank if each input and input-sequence maps the state set onto the same number of next states. CR-machines are analysed, using their sequential closure (semigroup), which is shown to be a simple semigroup, that is: a semi-direct product ( × ) |> of a left- and a right-copy semigroup, and a group. So in general a CR-machine is a composition of: a , a and a machine, which are three of the five basic types of state machines to be derived [1]