Pseudodeterministic Communication Complexity

Abstract

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 $n^{\hat{I}\text{c◯}(1)}$. 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.