A transformation semigroup is a pair (Q;S) consisting of a finite set Q, a finite semigroupS and a semigroup action λ : Q X SQ, (q, s s(q) which means : i) q 𝜖Q,s, t 𝜖S : st (q) = s (t (q)) , and (ii) s, t 𝜖Sq 𝜖Q, s (q) = t (q)s = t. A state machine or a semiautomation is an ordered triple M = (Q, ∑, F ), where Q and are finite sets and F : Q X ∑Qis a partial function. This paper provides the construction of state machines associate a direct product, the cascade product, and wreath product of transformations semigroups.
