文章基本信息

标题：Nearly Optimal Separations Between Communication (or Query) Complexity and Partitions
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作者：Andris Ambainis ; Martins Kokainis ; Robin Kothari 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2016
卷号：50
页码：4:1-4:14
DOI：10.4230/LIPIcs.CCC.2016.4
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We show a nearly quadratic separation between deterministic communication complexity and the logarithm of the partition number, which is essentially optimal. This improves upon a recent power 1.5 separation of Göös, Pitassi, and Watson (FOCS 2015). In query complexity, we establish a nearly quadratic separation between deterministic (and even randomized) query complexity and subcube partition complexity, which is also essentially optimal. We also establish a nearly power 1.5 separation between quantum query complexity and subcube partition complexity, the first superlinear separation between the two measures. Lastly, we show a quadratic separation between quantum query complexity and one-sided subcube partition complexity. Our query complexity separations use the recent cheat sheet framework of Aaronson, Ben-David, and Kothari. Our query functions are built up in stages by alternating function composition with the cheat sheet construction. The communication complexity separation follows from "lifting" the query separation to communication complexity.
关键词：Query Complexity; Communication Complexity; Subcube Partition Complexity; Partition Bound