Classes of Bounded Counting Type and their Inclusion Relations

Classes of bounded counting type are a generalization of complexity classes with finite acceptance types. The latter ones are defined via nondeterministic machines whose number of accepting paths up to a certain maximum is responsible for the question of acceptance of the input. For the classes of bounded counting type each computation path may have one of k possible results from the set {0,⋯, k-1} (k≥2), and we count the number of paths having result 1, as well as the number of paths having result 2, etc. Each result (except 0) is counted up to a certain maximum, and the vector formed by these numbers is responsible for the acceptance question.

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