ORACLES THAT COMPUTE VALUES

This paper focuses on complexity classes of partial functions that are computed in polynomial time with oracles in NPMV, the class of all mu ltivalued partial functions that are computable nondeterministically i n polynomial time. Concerning deterministic polynomial-time reducibili ties, it is shown that 1. a multivalued partial function is polynomial -time computable with k adaptive queries to NPMV if and only if it is polynomial-time computable via 2(k) - 1 nonadaptive queries to NPMV; 2 . a characteristic function is polynomial-time computable with k adapt ive queries to NPMV if and only if it is polynomial-time computable wi th k adaptive queries to NP; 3. unless the Boolean hierarchy collapses , for every k, Ic adaptive (nonadaptive) queries to NPMV are different than k + 1 adaptive (nonadaptive) queries to NPMV. Nondeterministic r educibilities, lowness, and the difference hierarchy over NPMV are als o studied. The difference hierarchy for partial functions does not col lapse unless the Boolean hierarchy collapses, but, surprisingly, the l evels of the difference and bounded query hierarchies do not interleav e (as is the case for sets) unless the polynomial hierarchy collapses.