Pseudodeterministic Communication Complexity

2025-11-06

AI Summary

This work resolves the open question of whether an exponential separation exists between pseudodeterministic and randomized communication complexity: it constructs a partial function on $n$-bit inputs whose randomized communication complexity is $O(log n)$, yet every total-function extension requires $Omega(n^c)$ randomized communication complexity for some constant $c > 0$. Leveraging lifting techniques, the authors extend Gavinsky’s (2025) lower bound from the parity decision tree model to the two-party communication setting—achieving the first exponential separation between pseudodeterministic and randomized protocols in the standard two-party communication model. This result establishes a fundamental limitation on the communication efficiency of pseudodeterministic protocols and advances our understanding of the role of randomness in distributed computation.

Technology Category

Machine Learning: Probabilistic Circuits and Graphical ModelsMultiagent Systems: Agent CommunicationReasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

Security and Privacy: Privacy-enhancing technologiesGraph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• Exhibits a partial function with logarithmic randomized communication complexity
• Shows total function completions require exponentially higher communication cost
• Establishes exponential separation between randomized and pseudodeterministic protocols

Innovation

• Pseudodeterministic communication complexity separation
• Lifting techniques from parity decision trees
• Exponential gap between randomized protocols