Complexity Classes with Finite Acceptance Types

Complexity classes with finite acceptance types are those classes that can be obtained by nondeterministic machines, if the global acceptance condition is of the form: the number of accepting computation paths is in the set A, for some fixed finite 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.

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