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• W3037028364 abstract "$ newcommand{sdisj}{textsf{Set-Disjointness}} $ We study $sdisj$ in a generalized model of randomized two-party communication where the probability of acceptance must be at least $alpha(n)$ on yes-inputs and at most $beta(n)$ on no-inputs, for some functions $alpha(n)> beta(n)$. Our main result is a complete characterization of the private-coin communication complexity of $sdisj$ for all functions $alpha$ and $beta$, and a near-complete characterization for public-coin protocols. In particular, we obtain a simple proof of a theorem of Braverman and Moitra (STOC 2013), who studied the case where $alpha=1/2+epsilon(n)$ and $beta=1/2-epsilon(n)$. The following contributions play a crucial role in our characterization and are interesting in their own right. We introduce two communication analogues of the classical complexity class that captures small bounded-error computations: we define a “restricted” class $mathsf{SBP}$ (which lies between $mathsf{MA}$ and $mathsf{AM}$) and an “unrestricted” class $mathsf{USBP}$. The distinction between them is analogous to the distinction between the well-known communication classes $mathsf{PP}$ and $mathsf{UPP}$. We show that the $mathsf{SBP}$ communication complexity is precisely captured by the classical corruption lower bound method. This sharpens a theorem of Klauck (CCC 2003). We use information complexity arguments to prove a linear lower bound on the $mathsf{USBP}$ complexity of $sdisj$. <! -- Footnote > A preliminary version of this paper appeared in the Proceedings of the 18th International Workshop on Randomization and Computation (RANDOM), 2014." @default.
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• W3037028364 date "2016-01-01" @default.
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• W3037028364 doi "https://doi.org/10.4086/toc.2016.v012a009" @default.
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