We consider the following question of bounded simultaneous messages (BSM) protocols: Can computationally unbounded Alice and Bob evaluate a function $f(x,y)$ of their inputs by sending polynomial-size messages to a computationally bounded Carol? The special case where $f$ is the mod-2 inner-product function and Carol is bounded to AC$^0$ has been studied in previous works. The general question can be broadly motivated by applications in which distributed computation is more costly than local computation, including secure two-party computation. In this work, we initiate a more systematic study of the BSM model, with different functions $f$ and computational bounds on Carol. In particular, we give evidence against the existence of BSM protocols with polynomial-size Carol for naturally distributed variants of NP-complete languages.

翻译：我们考虑以下有界同时通信（BSM）协议问题：计算能力无界的Alice和Bob能否通过向计算能力有界的Carol发送多项式大小的消息，来评估其输入的某个函数$f(x,y)$？其中$f$为模2内积函数且Carol的计算能力限制为AC$^0$的特例已在先前工作中被研究。该广义问题可广泛适用于分布式计算比本地计算成本更高的应用场景，包括安全两方计算。在本工作中，我们系统性地研究了BSM模型，考虑不同的函数$f$以及Carol的不同计算能力限制。特别地，我们给出了反对存在针对NP完全语言的自然分布式变体、且Carol具有多项式大小消息的BSM协议的证据。