Comparing Reductions to NP-Complete Sets

John M. Hitchcock, Aduri Pavan

Abstract: Under the assumption that NP does not have p-measure 0, we investigate reductions to NP-complete sets and prove the following: 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.