Publication

Pseudodeterministic Communication Complexity

2026

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 Ω (1). In particular, this shows an exponential separation between randomized and 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. CCS Concepts • Theory of computation → Communication complexity; Oracles and decision trees.

Official source

https://infoscience.epfl.ch/entities/publication/6c21f6ba-c306-4e10-8132-c84f39f6b9d5

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2026

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/6c21f6ba-c306-4e10-8132-c84f39f6b9d5

About this result

Related concepts (32)

Communication complexity

In theoretical computer science, communication complexity studies the amount of communication required to solve a problem when the input to the problem is distributed among two or more parties. The study of communication complexity was first introduced by Andrew Yao in 1979, while studying the problem of computation distributed among several machines. The problem is usually stated as follows: two parties (traditionally called Alice and Bob) each receive a (potentially different) -bit string and .

Computational complexity theory

In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used.

Computational complexity

In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory.

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