Complexity Classes with Finite Acceptance Types

Complexity classes with nite acceptance types are the classes obtained by nonde-terministic machines, if the global acceptance condition is of the form: the number of accepting computation paths is in the set A, for some xed nite set A. We study the relationships between such classes, exhibiting conditions, under which one class is contained in another one relative to all oracles, or conversely there is an oracle seperation. The proof technique uses a key lemma which transforms the inclusionship question for these classes into an existence question for certain hypergraphs.