2026-07-19T19:37:34Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:4367 2024-03-06T10:34:57Z ddc:004 open_access

A Strong Direct Product Theorem for the Tribes Function via the Smooth-Rectangle Bound Harsha, Prahladh Jain, Rahul Rectangle bound Tribes function Strong direct product The main result of this paper is an optimal strong direct product result for the two-party public-coin randomized communication complexity of the Tribes function. This is proved by providing an alternate proof of the optimal lower bound of Omega(n) for the randomised communication complexity of the Tribes function using the so-called smooth-rectangle bound, introduced by Jain and Klauck [CCC/2010]. The optimal Omega(n) lower bound for Tribes was originally proved by Jayram, Kumar and Sivakumar [STOC/2003], using a more powerful lower bound technique, namely the information complexity bound. The information complexity bound is known to be at least as strong a lower bound method as the smooth-rectangle bound [Kerenidis et al, 2012]. On the other hand, we are not aware of any function or relation for which the smooth-rectangle bound is (asymptotically) smaller than its public-coin randomized communication complexity. The optimal direct product for Tribes is obtained by combining our smooth-rectangle bound for tribes with the strong direct product result of Jain and Yao (2012) in terms of smooth-rectangle bound. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Prahladh Harsha and Rahul Jain 2013 Is Part Of LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2013.141 urn:nbn:de:0030-drops-43670 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.141 eng https://creativecommons.org/licenses/by/3.0/legalcode