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

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

2001-03-19

arxiv.org/abs/math/0103112v2

Mathematics

General Mathematics

12 pages. Publ.: IFIP Workshop on "Logic and Architecture Synthesis", May 1990, Paris (digest publ: North-Holland, p167-176).

Scientific paper

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 \times 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.

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