2012 IEEE 27th Conference on Computational Complexity (1996)

Philadelphia, PA

May 24, 1996 to May 27, 1996

ISBN: 0-8186-7386-9

pp: 59

Joan Feigenbaum , AT & T Research

ABSTRACT

Lance Fortnow, Sophie Laplante, and Ashish V. Naik We address two questions about self-reducibility--the power of adaptiveness in examiners that take advice and the relationship between random-self-reducibility and self-correctability. We first show that adaptive examiners are more powerful than nonadaptive examiners, even if the nonadaptive ones are nonuniform. Blum et al. [Blum, Luby and Rubinfeld, Journal of Computer and System Sciences, 59:549--595, 1993] showed that every random-self-reducible function is self-correctable. However, whether self-correctability implies random-self-reducibility is unknown. We show that, under a reasonable complexity hypothesis, there exists a self-correctable function that is not random-self-reducible. For P-sampleable distributions, however, we show that constructing a self-correctable function that is not random-self-reducible is as hard as proving that P is not equal to PP.

INDEX TERMS

Computational complexity, coherence, self-correctability, random-self-reducibility, polynomial advice, Kolmogorov complexity, adaptive versus nonadaptive oracle machines

CITATION

Joan Feigenbaum,
"On Coherence, Random-Self-Reducibility, and Self-Correction",

*2012 IEEE 27th Conference on Computational Complexity*, vol. 00, no. , pp. 59, 1996, doi:10.1109/CCC.1996.507668