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The Power of Natural Properties as Oracles

Authors Russell Impagliazzo, Valentine Kabanets, Ilya Volkovich

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
Keywords
  • natural properties
  • Minimal Circuit Size Problem (MCSP)
  • circuit lower bounds
  • hardness of MCSP
  • learning algorithms
  • obfuscation
  • Indistinguishability Obfuscators (IO)

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Abstract

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.

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Russell Impagliazzo, Valentine Kabanets, and Ilya Volkovich. The Power of Natural Properties as Oracles. In 33rd Computational Complexity Conference (CCC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 102, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.CCC.2018.7

Author Details

Russell Impagliazzo
  • Department of Computer Science, University of California San Diego, La Jolla, CA, USA
Valentine Kabanets
  • School of Computing Science, Simon Fraser University, Burnaby, BC, Canada
Ilya Volkovich
  • Department of EECS, CSE Division, University of Michigan, Ann Arbor, MI, USA

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