@inproceedings{04ab0a822263492b8bc20e2e1bfc7e29,

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 = "https://doi.org/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",

}