eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-06-04
7:1
7:20
10.4230/LIPIcs.CCC.2018.7
article
The Power of Natural Properties as Oracles
Impagliazzo, Russell
1
Kabanets, Valentine
2
Volkovich, Ilya
3
Department of Computer Science, University of California San Diego, La Jolla, CA, USA
School of Computing Science, Simon Fraser University, Burnaby, BC, Canada
Department of EECS, CSE Division, University of Michigan, Ann Arbor, MI, USA
We study the power of randomized complexity classes that are given oracle access to a natural property of Razborov and Rudich (JCSS, 1997) or its special case, the Minimal Circuit Size Problem (MCSP). We show that in a number of complexity-theoretic results that use the SAT oracle, one can use the MCSP oracle instead. For example, we show that ZPEXP^{MCSP} !subseteq P/poly, which should be contrasted with the previously known circuit lower bound ZPEXP^{NP} !subseteq P/poly. We also show that, assuming the existence of Indistinguishability Obfuscators (IO), SAT and MCSP are equivalent in the sense that one has a ZPP algorithm if and only the other one does. We interpret our results as providing some evidence that MCSP may be NP-hard under randomized polynomial-time reductions.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol102-ccc2018/LIPIcs.CCC.2018.7/LIPIcs.CCC.2018.7.pdf
natural properties
Minimal Circuit Size Problem (MCSP)
circuit lower bounds
hardness of MCSP
learning algorithms
obfuscation
Indistinguishability Obfuscators (IO)