2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61101Constant 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.12 pages. Publ.: IFIP Workshop on "Logic and Architecture Synthesis", May 1990, Paris (digest publ: North-Holland, p167-176). See http://www.iae.nl/users/benschop/c-ranksm.dvi, and http://www.iae.nl/users/benschop/ism.htm (on integer state machines M[Z,A]) and http://www.iae.nl/users/benschop/cantor.htm (on 2^N < Z! = {a,b}*/Z). --- V2 corr: thm4.1cGeneral Mathematics20M35, 03D05, 68Q70text