Finite Semigroups of Constant Rank, and the Five Basic State Machine Types

Constant Rank () 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. -machines are analysed via their sequential closure (semigroup), which is a a semi-direct product ( × ) * of a left- and a right-copy semigroup, and a group. So in general a -machine is a composition of: a , a and a machine, which are three of the five basic types of state machines [1]. (Original title: ”The Structure of Constant Rank State Machines”)