A note on the partition bound for one-way classical communication complexity

02/21/2023

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by   Srinivasan Arunachalam, et al.

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National University of Singapore

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ibm

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We present a linear program for the one-way version of the partition bound (denoted 𝗉𝗋𝗍^1_ε(f)). We show that it characterizes one-way randomized communication complexity 𝖱_ε^1(f) with shared randomness of every partial function f:𝒳×𝒴→𝒵, i.e., for δ,ε∈(0,1/2), 𝖱_ε^1(f) ≥log𝗉𝗋𝗍_ε^1(f) and 𝖱_ε+δ^1(f) ≤log𝗉𝗋𝗍_ε^1(f) + loglog(1/δ). This improves upon the characterization of 𝖱_ε^1(f) in terms of the rectangle bound (due to Jain and Klauck, 2010) by reducing the additive O(log(1/δ))-term to loglog(1/δ).