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.
|Original language||American English|
|Title of host publication||35th Computational Complexity Conference, CCC 2020|
|Publisher||Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing|
|State||Published - 1 Jul 2020|
|Event||35th Computational Complexity Conference, CCC 2020 - Virtual, Online, Germany|
Duration: 28 Jul 2020 → 31 Jul 2020
|Name||Leibniz International Proceedings in Informatics, LIPIcs|
|Conference||35th Computational Complexity Conference, CCC 2020|
|Period||28/07/20 → 31/07/20|
Bibliographical noteFunding Information:
Funding Yuval Filmus: Supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 802020-ERC-HARMONIC. Yuval Ishai: Supported by ERC Project NTSC (742754), NSF-BSF grant 2015782, BSF grant 2018393, and a grant from the Ministry of Science and Technology, Israel and Department of Science and Technology, Government of India. Avi Kaplan: Supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 802020-ERC-HARMONIC, and ERC Project NTSC (742754).
© Yuval Filmus, Yuval Ishai, Avi Kaplan, and Guy Kindler; licensed under Creative Commons License CC-BY 35th Computational Complexity Conference (CCC 2020).
- Communication complexity
- Simultaneous messages