On the Retracts Of Automata on Directed Complete Posets

Automata Theory is an exciting branch of Computer Science and Discrete Mathematics. The algebraic theory of a particular type of automata (without outputs) is nothing but the actions of a free monoid or a free semigroup on a set (of states). On the other hand, Domain Theory, which studies directed complete partially ordered sets was introduced by Scott and has grown into a respected field on the borderline between Mathematics and Computer Science. In this paper, combining the above two notions, we consider automata on domains and study the algebraic notion of retract with respect to classes of monomorphisms for automata on directed complete posets.