Polynomial-Time Multi-Selectivity

Details Polynomial-Time Multi-Selectivity Polynomial-Time Multi-Selectivity

1999-07-25

arxiv.org/abs/cs/9907034v1

Journal of Universal Computer Science vol. 3, no. 3, pp. 197--229, 1997

Computer Science

Computational Complexity

40 pages

Scientific paper

We introduce a generalization of Selman's P-selectivity that yields a more flexible notion of selectivity, called (polynomial-time) multi-selectivity, in which the selector is allowed to operate on multiple input strings. Since our introduction of this class, it has been used to prove the first known (and optimal) lower bounds for generalized selectivity-like classes in terms of EL_2, the second level of the extended low hierarchy. We study the resulting selectivity hierarchy, denoted by SH, which we prove does not collapse. In particular, we study the internal structure and the properties of SH and completely establish, in terms of incomparability and strict inclusion, the relations between our generalized selectivity classes and Ogihara's P-mc (polynomial-time membership-comparable) classes. Although SH is a strictly increasing infinite hierarchy, we show that the core results that hold for the P-selective sets and that prove them structurally simple also hold for SH. In particular, all sets in SH have small circuits; the NP sets in SH are in Low_2, the second level of the low hierarchy within NP; and SAT cannot be in SH unless P = NP. Finally, it is known that P-Sel, the class of P-selective sets, is not closed under union or intersection. We provide an extended selectivity hierarchy that is based on SH and that is large enough to capture those closures of the P-selective sets, and yet, in contrast with the P-mc classes, is refined enough to distinguish them.

Affiliated with

Also associated with

No associations

Rating

Polynomial-Time Multi-Selectivity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Polynomial-Time Multi-Selectivity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Polynomial-Time Multi-Selectivity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-619281