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Comparing Reductions to NP-Complete Sets John M. Hitchcock 1
 

Summary: Comparing Reductions to NP-Complete 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 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 re-
ductions: 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 many-one complete problem for
NE is complete under one-to-one, length-increasing reductions that are computed

  

Source: Aduri, Pavan - Department of Computer Science, Iowa State University

 

Collections: Computer Technologies and Information Sciences