同时消息传递模型的新结果
New Results in the Simultaneous Message Passing Model
摘要：
考虑以下用于计算X X Y X Z的子集的关系f的同时消息传递（SMP）模型。在这个模型中，Alice在X中的输入x上，Bob在Y中的输入y上，向第三方Reynolds发送一条消息，然后Reynolds输出Z中的z，使得f中的（x，y，z）。我们首先显示最佳的“直和”的结果，在这个模型中的所有关系f，无论是在量子和经典的设置，在这种情况下，我们允许共享资源（共享纠缠在量子协议和公共硬币在经典协议）之间的爱丽丝和Reynolds和鲍勃和Reynolds和没有共享资源之间的爱丽丝和鲍勃。这意味着，在这个模型中，计算f的k个同时实例所需的通信，总体上是恒定成功的，至少是计算一个实例所需的通信的k倍。这特别暗示了Chakrabarti，Shi，Wirth和Yao在2001年针对等式函数（以及一类其他所谓的鲁棒函数）给出的早期直和结果，在任何方之间没有共享资源的经典SMP模型中。此外，我们调查之间的差距smp模型和单向模型的通信复杂性，并展示了一个部分函数，是指数更昂贵的，在前者，如果量子通信纠缠是允许的，相比后者，即使在确定性的情况下。
英文摘要：
Consider the following Simultaneous Message Passing (SMP) model for computing a relation f subset of X x Y x Z. In this model Alice, on input x in X and Bob, on input y in Y, send one message each to a third party Referee who then outputs a z in Z such that (x,y,z) in f. We first show optimal 'Direct sum' results for all relations f in this model, both in the quantum and classical settings, in the situation where we allow shared resources (shared entanglement in quantum protocols and public coins in classical protocols) between Alice and Referee and Bob and Referee and no shared resource between Alice and Bob. This implies that, in this model, the communication required to compute k simultaneous instances of f, with constant success overall, is at least k-times the communication required to compute one instance with constant success. This in particular implies an earlier Direct sum result, shown by Chakrabarti, Shi, Wirth and Yao, 2001, for the Equality function (and a class of other so-called robust functions), in the classical smp model with no shared resources between any parties. Furthermore we investigate the gap between the smp model and the one-way model in communication complexity and exhibit a partial function that is exponentially more expensive in the former if quantum communication with entanglement is allowed, compared to the latter even in the deterministic case.
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