Polynomial time algorithms for inclusion and equivalence of deterministic omega acceptors

The class of omega languages recognized by deterministic parity acceptors (DPAs) or deterministic Muller acceptors (DMAs) is exactly the regular omega languages. The inclusion problem is the following: given two acceptors A₁ and A₂, determine whether the language recognized by A₁ is a subset of the language recognized by A₂, and if not, return an ultimately periodic omega word accepted by A₁ but not A₂. We describe polynomial time algorithms to solve this problem for two DPAs and for two DMAs. Corollaries include polynomial time algorithms to solve the equivalence problem for DPAs and DMAs, and also the inclusion and equivalence problems for deterministic Buechi and coBuechi acceptors.