 
Summary: Comparing Reductions to NPComplete Sets
John M. Hitchcock 1
Department of Computer Science
University of Wyoming
A. Pavan 2
Department of Computer Science
Iowa State University
Abstract
Under the assumption that NP does not have pmeasure 0, we investigate reductions
to NPcomplete sets and prove the following:
(1) Adaptive reductions are more powerful than nonadaptive reductions: there is
a problem that is Turingcomplete for NP but not truthtablecomplete.
(2) Strong nondeterministic reductions are more powerful than deterministic re
ductions: there is a problem that is SNPcomplete for NP but not Turing
complete.
(3) Every problem that is manyone complete for NP is complete under length
increasing reductions that are computed by polynomialsize circuits.
The first item solves one of Lutz and Mayordomo's "Twelve Problems in Resource
Bounded Measure" (1999). We also show that every manyone complete problem for
NE is complete under onetoone, lengthincreasing reductions that are computed
