2026-07-24T00:57:14Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:7517 2024-03-06T10:40:12Z ddc:004 open_access

Trading Information Complexity for Error Dagan, Yuval Filmus, Yuval Hatami, Hamed Li, Yaqiao communication complexity information complexity We consider the standard two-party communication model. The central problem studied in this article is how much can one save in information complexity by allowing a certain error. * For arbitrary functions, we obtain lower bounds and upper bounds indicating a gain that is of order Omega(h(epsilon)) and O(h(sqrt{epsilon})). Here h denotes the binary entropy function. * We analyze the case of the two-bit AND function in detail to show that for this function the gain is Theta(h(epsilon)). This answers a question of Braverman et al. [Braverman, STOC 2013]. * We obtain sharp bounds for the set disjointness function of order n. For the case of the distributional error, we introduce a new protocol that achieves a gain of Theta(sqrt{h(epsilon)}) provided that n is sufficiently large. We apply these results to answer another of question of Braverman et al. regarding the randomized communication complexity of the set disjointness function. * Answering a question of Braverman [Braverman, STOC 2012], we apply our analysis of the set disjointness function to establish a gap between the two different notions of the prior-free information cost. In light of [Braverman, STOC 2012], this implies that amortized randomized communication complexity is not necessarily equal to the amortized distributional communication complexity with respect to the hardest distribution. As a consequence, we show that the epsilon-error randomized communication complexity of the set disjointness function of order n is n[C_{DISJ} - Theta(h(epsilon))] + o(n), where C_{DISJ} ~ 0.4827$ is the constant found by Braverman et al. [Braverman, STOC 2012]. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Yuval Dagan and Yuval Filmus and Hamed Hatami and Yaqiao Li 2017 Is Part Of LIPIcs, Volume 79, 32nd Computational Complexity Conference (CCC 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CCC.2017.16 urn:nbn:de:0030-drops-75179 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2017.16 eng https://creativecommons.org/licenses/by/3.0/legalcode