On using oracles that compute values
A multivalued partial function is polynomial-time computable with k adaptive queries to NPMV if and only if it is polynomial-time computable via 2k — 1 nonadaptive queries to NPMV.
A characteristic function is polynomial-time computable with k adaptive queries to NPMV if and only if it is polynomial-time computable with k adaptive queries to NP.
Unless the Boolean hierarchy collapses, k adaptive (nonadaptive) queries to NPMV is different than k+1 adaptive (nonadaptive) queries to NPMV for every k.
Nondeterministic reducibilities, lowness and the difference hierarchy over NPMV are also studied. The difference hierarchy for partial functions does not collapse unless the Boolean hierarchy collapses, but, surprisingly, the levels of the difference and bounded query hierarchies do not interleave (as is the case for sets) unless the polynomial hierarchy collapses.
KeywordsPolynomial Time Partial Function Input String Satisfying Assignment Polynomial Hierarchy
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