Pseudodeterministic Communication Complexity

TL;DR

This paper demonstrates an exponential separation between randomized and pseudodeterministic communication complexities using a constructed partial function, highlighting fundamental differences in computational models.

Contribution

It introduces a partial function with low randomized complexity that resists efficient total completion, extending prior parity decision tree results to communication complexity.

Findings

Existence of an n-bit partial function with O(log n) randomized complexity

Any total completion requires n^{Ω(1)}} randomized communication

Shows exponential separation between randomized and pseudodeterministic protocols

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 $n^{\Omega(1)}$. 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.