Elsevier

Theoretical Computer Science

Volume 19, Issue 3, September 1982, Pages 287-304
Theoretical Computer Science

Reductions on NP and P-selective sets

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Abstract

P-selective sets are used to distinguish polynomial time-bounded reducibilities on NP. In particular, we consider different kinds of “positive” reductions; these preserve membership in NP and are not a priori closed under complements. We show that the class of all sets which are both P-selective and have positive reductions to their complements is P. This is used to show that if DEXTNEXT, then there exists a set in NP−P that is not positive reducible to its complement. Various similar results are obtained. We also show that P is the class of all sets which are both p-selective and positive truth-table self-reducible. From this result, it follows that various naturally defined apparently intractible problems are not p-selective unless P = NP.

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This research was supported in part by the National Science Foundation under grant MCS77- 23493 AO2.