Concrete constructions of noncommutative free dcpo semigroups

Free dcpo semigroups play an important role in modeling the semantics of nondeterministic programming languages. In this paper, we provide concrete constructions for free dcpo semigroups, free domain bands (with additional inequalities), and free dcpo groups. They are the noncommutative generalizations of the classical Plotkin (Smyth, Hoare) powerdomains.