ECCC-Report TR06-039https://eccc.weizmann.ac.il/report/2006/039Comments and Revisions published for TR06-039en-usSun, 19 Mar 2006 20:08:24 +0200
Paper TR06-039
| Comparing Reductions to NP-Complete Sets |
John Hitchcock,
A. Pavan
https://eccc.weizmann.ac.il/report/2006/039Under the assumption that NP does not have p-measure 0, we
investigate reductions to NP-complete sets and prove the following:
- Adaptive reductions are more powerful than nonadaptive
reductions: there is a problem that is Turing-complete for NP but
not truth-table-complete.
- Strong nondeterministic reductions are more powerful than
deterministic reductions: there is a problem that is SNP-complete
for NP but not Turing-complete.
- 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.
Sun, 19 Mar 2006 20:08:24 +0200https://eccc.weizmann.ac.il/report/2006/039