In this paper, we propose a new conjecture, the XOR-KRW conjecture, which is a relaxation of the Karchmer-Raz-Wigderson conjecture [Mauricio Karchmer et al., 1995]. This relaxation is still strong enough to imply 𝐏 ̸ ⊆ NC¹ if proven. We also present a weaker version of this conjecture that might be used for breaking n³ lower bound for De Morgan formulas. Our study of this conjecture allows us to partially answer an open question stated in [Dmitry Gavinsky et al., 2017] regarding the composition of the universal relation with a function. To be more precise, we prove that there exists a function g such that the composition of the universal relation with g is significantly harder than just a universal relation. The fact that we can only prove the existence of g is an inherent feature of our approach. The paper’s main technical contribution is a new approach to lower bounds for multiplexer-type relations based on the non-deterministic hardness of non-equality and a new method of converting lower bounds for multiplexer-type relations into lower bounds against some function. In order to do this, we develop techniques to lower bound communication complexity in half-duplex and partially half-duplex communication models.
@InProceedings{mihajlin_et_al:LIPIcs.CCC.2021.38, author = {Mihajlin, Ivan and Smal, Alexander}, title = {{Toward Better Depth Lower Bounds: The XOR-KRW Conjecture}}, booktitle = {36th Computational Complexity Conference (CCC 2021)}, pages = {38:1--38:24}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-193-1}, ISSN = {1868-8969}, year = {2021}, volume = {200}, editor = {Kabanets, Valentine}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2021.38}, URN = {urn:nbn:de:0030-drops-143121}, doi = {10.4230/LIPIcs.CCC.2021.38}, annote = {Keywords: communication complexity, KRW conjecture, circuit complexity, half-duplex communication complexity, Karchmer-Wigderson games, multiplexer relation, universal relation} }
Feedback for Dagstuhl Publishing