基于求和算子的XOR对策的通信复杂性
The communication complexity of XOR games via summing operators
摘要：
差异法被广泛用于寻找异或博弈的通信复杂性的下界。众所周知，这些界限可能远非最佳。在这种情况下，不相交性通常被认为是该方法无法给出好的边界的情况，因为游戏的值的增量在通信位的数量上是线性的（而不是指数的）。本文证明了异或博弈的存在性，其中差异方法产生的边界差，因为一个愿望。事实上，我们证明了存在这样的游戏与任何先前规定的值。为了证明这一结果，我们应用p-求和算子理论，这是Banach空间理论中的一个中心话题。我们在该文件中显示的其他应用这一理论的研究的通信复杂性的XOR游戏。
英文摘要：
The discrepancy method is widely used to find lower bounds for communication complexity of XOR games. It is well known that these bounds can be far from optimal. In this context Disjointness is usually mentioned as a case where the method fails to give good bounds, because the increment of the value of the game is linear (rather than exponential) in the number of communicated bits. We show in this paper the existence of XOR games where the discrepancy method yields bounds as poor as one desires. Indeed, we show the existence of such games with any previously prescribed value. To prove this result we apply the theory of p-summing operators, a central topic in Banach space theory. We show in the paper other applications of this theory to the study of the communication complexity of XOR games.
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