Monoid-matrix type automata

Monoid-matrix type automata are introduced and studied in this paper. We give a characterization of the cyclic monoid-matrix type automata and the regular monoid-matrix type automata. Also, we provide a method to determine the structures of canonical Sℓ-automata (canonical C-automata, respectively) whose endomorphism monoids are isomorphic to a given finite meet semilattice with the greatest element (Clifford monoid, respectively).