@inproceedings{00bf6642d6574686b798780ec2b54a76,
title = "Average-case lower bounds for formula size",
abstract = "We give an explicit function h : {0; 1}n → {0; 1} such that any deMorgan formula of size O(n2.499) agrees with h on at most 1 2 + ε fraction of the inputs, where ε is exponentially small (i.e. ε = 2-nΩ(1) ). We also show, using the same technique, that any boolean formula of size O(n1.999) over the complete basis, agrees with h on at most 1 2 +ε fraction of the inputs, where ε is exponentially small (i.e. ε = 2-nΩ(1) ). Our construction is based on Andreev's (n2.5-o(1)) formula size lower bound that was proved for the case of exact computation [2].",
keywords = "Average-case hardness, Boolean formulas, Correlation bounds, Demorgan formulas, Lower bounds",
author = "Ilan Komargodski and Ran Raz",
year = "2013",
doi = "10.1145/2488608.2488630",
language = "American English",
isbn = "9781450320290",
series = "Proceedings of the Annual ACM Symposium on Theory of Computing",
pages = "171--180",
booktitle = "STOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing",
note = "45th Annual ACM Symposium on Theory of Computing, STOC 2013 ; Conference date: 01-06-2013 Through 04-06-2013",
}