Structure of Constant Rank State Machines, and the Five Basic State Machine Types
Nico F. Benschop · SSRN Electronic Journal · 2002
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].