Non-Uniform Reductions

Reductions and completeness notions form the heart of computational complexity theory. Recently non-uniform reductions have been naturally introduced in a variety of settings concerning completeness notions for NP and other classes. We follow up on these results by strengthening some of them. In particular, we show that under certain well studied hypotheses: • many-one complete sets for NP are length increasing complete with a single bit of advice, strengthening a result of Hitchcock and Pavan [HP06]. • 1-truth-table complete sets for NP are many-one complete with a single bit of advice. We tighten another result of [HP06] and give a trade-off between the amount of advice that is needed for the reduction and its honesty, i.e., how length decreasing a reduction is for the many-one complete degree of NEXP. We also construct an oracle relative to which this trade-off is optimal. For uniform reductions, the trade-off only yields exponential honesty and the oracle witnesses an expon...

• Type: Journal
• Year: 2010
• Where: MST
• Authors: Harry Buhrman, Benjamin J. Hescott, Steven Homer, Leen Torenvliet
• Keywords: Completeness Notions, Many-one, MST 2010, Reductions