Finite Semigroups of Constant Rank, and the five Basic State Machine types

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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 via their sequential closure (semigroup), which is a simple semigroup, thus: a semi- direct product (L × R)*G of a left- and a right-copy semigroup, and a group.... So in general a CR-machine is a composition of: a branch-, a reset- and a permutation machine, which are three of the five basic types of state machines, to be derived.