@inproceedings{b15ffe4308a9457b9fe93a70aaef213d,
title = "Limits of preprocessing",
abstract = "It is a classical result that the inner product function cannot be computed by an AC0 circuit [17, 1, 22]. It is conjectured that this holds even if we allow arbitrary preprocessing of each of the two inputs separately. We prove this conjecture when the preprocessing of one of the inputs is limited to output n + n/(logω(1) n) bits. Our methods extend to many other functions, including pseudorandom functions, and imply a (weak but nontrivial) limitation on the power of encoding inputs in low-complexity cryptography. Finally, under cryptographic assumptions, we relate the question of proving variants of the main conjecture with the question of learning AC0 under simple input distributions.",
keywords = "Circuit, Communication complexity, IPPP, PRF, Preprocessing, Simultaneous messages",
author = "Yuval Filmus and Yuval Ishai and Avi Kaplan and Guy Kindler",
note = "Publisher Copyright: {\textcopyright} Yuval Filmus, Yuval Ishai, Avi Kaplan, and Guy Kindler; licensed under Creative Commons License CC-BY 35th Computational Complexity Conference (CCC 2020).; 35th Computational Complexity Conference, CCC 2020 ; Conference date: 28-07-2020 Through 31-07-2020",
year = "2020",
month = jul,
day = "1",
doi = "https://doi.org/10.4230/LIPIcs.CCC.2020.17",
language = "الإنجليزيّة",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
editor = "Shubhangi Saraf",
booktitle = "35th Computational Complexity Conference, CCC 2020",
}