Comparing Reductions to NP-Complete Sets

Under the assumption that NP does not have p-measure 0, we investigate reductions to NP-complete sets and 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 Turingcomplete. (3) Every problem that is many-one complete for NP is complete under lengthincreasing reductions that are computed by polynomial-size circuits. The first item solves one of Lutz and Mayordomo's "Twelve Problems in ResourceBounded Measure" (1999). We also show that every many-one complete problem for NE is complete under one-to-one, length-increasing reductions that are computed by polynomial-size circuits.

• Type: Journal
• Year: 2006
• Where: ECCC
• Authors: John M. Hitchcock, Aduri Pavan
• Keywords: ECCC 2006, Nonadaptive Reductions, Reductions, Strong Nondeterministic Reductions