  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.
