Comparing reductions to NP-complete sets

Abstract

Under the assumption that NP does riot have p-measure 0, we investigate reductions to NP-complete sets arid prove the following: 1. Adaptive reductions are more powerful than nonadaptive reductions: there is a problem that is Turing-complete for NP but not truth-table-complete. 2. Strong nondeterministic reductions are more powerful than deterministic reductions: there is a problem that is SNP-complete for NP but not Turing-complete. 3. Every problem that is many-one complete for NP is complete under length-increasing reductions that are computed by polynomial-size circuits. The first item solves one of Lutz and Mayordomo's "Twelve Problems in Resource-Bounded Measure" (1999). We also show that every problem that is complete for NE is complete under one-to-one, length-increasing reductions that are computed by polynomial-size circuits. © Springer-Verlag; Berlin Heidelberg 2006.