@inproceedings{5d970d9cc45549549ae22f111703638c,

title = "On using oracles that compute values",

abstract = "This paper focuses on complexity classes of partial functions that are computed in polynomial time with oracles in NPMV, the class of all multivalued partial functions that are computable nondeterministically in polynomial time. Concerning deterministic polynomial-time reducibilities, 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 2k-1 nonadaptive queries to NPMV. 2. 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. 3. 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.",

author = "Stephen Fenner and Steve Homer and Mitsunori Ogiwara and Selman, {Alan L.}",

year = "1993",

doi = "10.1007/3-540-56503-5_40",

language = "English (US)",

isbn = "9783540565031",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "399--407",

editor = "Patrice Enjalbert and Alain Finkel and Wagner, {Klaus W.}",

booktitle = "STACS 1993 - 10th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings",

note = "10th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1993 ; Conference date: 25-02-1993 Through 27-02-1993",

}