TY - GEN
T1 - Limits of preprocessing
AU - Filmus, Yuval
AU - Ishai, Yuval
AU - Kaplan, Avi
AU - Kindler, Guy
N1 - Publisher Copyright:
© Yuval Filmus, Yuval Ishai, Avi Kaplan, and Guy Kindler; licensed under Creative Commons License CC-BY 35th Computational Complexity Conference (CCC 2020).
PY - 2020/7/1
Y1 - 2020/7/1
N2 - 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.
AB - 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.
KW - Circuit
KW - Communication complexity
KW - IPPP
KW - PRF
KW - Preprocessing
KW - Simultaneous messages
UR - http://www.scopus.com/inward/record.url?scp=85089370285&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.CCC.2020.17
DO - 10.4230/LIPIcs.CCC.2020.17
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AN - SCOPUS:85089370285
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 35th Computational Complexity Conference, CCC 2020
A2 - Saraf, Shubhangi
T2 - 35th Computational Complexity Conference, CCC 2020
Y2 - 28 July 2020 through 31 July 2020
ER -