Improved average-case lower bounds for de Morgan formula size: Matching worst-case lower bound

Ilan Komargodski, Ilan Raz, Avishay Tal, Ran Raz

Research output: Contribution to journalArticlepeer-review

Abstract

We give an explicit function h : {0; 1}n → {0; 1} such that every de Morgan formula of size n3-o(1)=r2 agrees with h on at most a fraction of 1/2 + 2-ω(r) of the inputs. Our technical contributions include a theorem that shows that the "expected shrinkage" result of Hastad [SIAM J. Comput., 27 (1998), pp. 48-64] actually holds with very high probability (where the restrictions are chosen from a certain distribution that takes into account the structure of the formula), using ideas of Impagliazzo, Meka, and Zuckerman [Proceedings of FOCS, 2012, pp. 111-119].

Original languageAmerican English
Pages (from-to)37-57
Number of pages21
JournalSIAM Journal on Computing
Volume46
Issue number1
DOIs
StatePublished - 2017

Keywords

  • Average-case lower bound
  • Boolean formulas
  • Shrinkage

All Science Journal Classification (ASJC) codes

  • General Computer Science
  • General Mathematics

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