-Continuous Kleene ω-Algebras

International audienceWe define and study basic properties of *-continuous Kleene ω-algebras that involve a *-continuous Kleene algebra with a *-continuous action on a semimodule and an infinite product operation that is also *-continuous. We show that *-continuous Kleene ω-algebras give rise to iteration semiring-semimodule pairs, and that for Büchi automata over *-continuous Kleene ω-algebras, one can compute the associated infinitary power series