We exhibit an $n$-bit partial function with randomized communication complexity $O(\log n)$ but such that any completion of this function into a total one requires randomized communication complexity $n^{Ω(1)}$. In particular, this shows an exponential separation between randomized and \emph{pseudodeterministic} communication protocols. Previously, Gavinsky (2025) showed an analogous separation in the weaker model of parity decision trees. We use lifting techniques to extend his proof idea to communication complexity.

翻译：我们构造了一个 $n$ 位部分函数，其随机化通信复杂度为 $O(\log n)$，但将该函数补全为全函数后，其随机化通信复杂度需要 $n^{Ω(1)}$。特别地，这揭示了随机化通信协议与伪确定性通信协议之间的指数级分离。此前，Gavinsky (2025) 在较弱的奇偶决策树模型中展示了类似的分离结果。我们利用提升技术将其证明思想推广至通信复杂度领域。