DIMACS TR: 96-16

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

Authors: Joan Feigenbaum, Lance Fortnow, Sophie Laplante, Ashish 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.

This work was presented in preliminary form at the IEEE Conference on Computational Complexity, Philadelphia PA, May 1996.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-16.ps.gz

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