On Coherence, Random-Self-Reducibility, and Self-Correction

• Authors: Joan Feigenbaum
• Venue: CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
• Year: 1996

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.