TY - GEN

T1 - On using oracles that compute values

AU - Fenner, Stephen

AU - Homer, Steve

AU - Ogiwara, Mitsunori

AU - Selman, Alan L.

N1 - Funding Information:
NPMV is the set of all partial multivalued functions that are computed nondeterministically in polynomial time, and NPSV is the set of all partial functions Dept. of Computer Science, Portland, ME 04103. Research partially supported by the National Science Foundation under grant no. CCR-9209833. S Dept. of Computer Science, Boston, MA 01003. Research partially supported by the National Science Foundation under grant no. CCR-9103055 Dept. of Computer Science, University of Electro-Communications, Chofu-shi, Tokyo 182, Japan. Research performed while visiting at: Dept. of Computer Science, SUNY at Buffalo, Buffalo, NY 14260. Research partially supported by the National Science Foundation under grant no. CCR-9002292. II Dept. of Computer Science, SUNY at Buffalo, Buffalo, NY 14260. Research partially supported 1)3, the National Science Foundation under grant no. CCR-9002292.
Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1993.

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

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U2 - 10.1007/3-540-56503-5_40

DO - 10.1007/3-540-56503-5_40

M3 - Conference contribution

AN - SCOPUS:85029529223

SN - 9783540565031

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 399

EP - 407

BT - STACS 1993 - 10th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings

A2 - Enjalbert, Patrice

A2 - Finkel, Alain

A2 - Wagner, Klaus W.

PB - Springer Verlag

T2 - 10th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1993

Y2 - 25 February 1993 through 27 February 1993

ER -