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 language | English |
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Pages (from-to) | 37-57 |
Number of pages | 21 |
Journal | SIAM Journal on Computing |
Volume | 46 |
Issue number | 1 |
DOIs | |
State | Published - 2017 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2017 Society for Industrial and Applied Mathematics.
Keywords
- Average-case lower bound
- Boolean formulas
- Shrinkage