Polynomial-time Hierarchies on Some Classes of Functions (II)

Four polynomial-time hierarchies on functions are introduced, which are considered to be generalizations of Valiant's counting function class #P, class Span-P introduced by Kobler et al., Krentel's optimization function class Opt-P, and F2p. It is shown that our polynomial hierarchies of optimization functions are the same as that defined by Krentel. The relationships within every hierarchy and between them are studied.