Ghadbane, Nacer2019-05-142019-05-142019http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/13957A transformation semigroup is a pair (Q; S) consisting of a finite set Q, a finie semigroup S and a semigroup action λ : Q X S⟶ Q, (q, s ⟼ s (q) which means : (i) ∀q Q, ∀s, t S : st (q) = s (t (q)) , (ii) ∀s, t S,∀q Q, s (q) = t (q)⟹ s = t. A state machine or a semiautomation is an ordered triple M = (Q, Σ, F ), where Q and are finite sets and F : Q X Σ⟶ Q is a partial function. In this paper, we give the construction of state machines associate a direct product, the cascade product and wreath product of transformations semigroups.semigroup, semigroup action, morphism semigroup, transformation semi-group, state machine.Article