Half-duplex communication complexity with adversary can be less than the classical communication complexity

TL;DR

This paper demonstrates that for certain functions, half-duplex communication protocols with adversaries can achieve lower communication complexity than traditional classical protocols, revealing a fundamental difference between the models.

Contribution

The paper provides the first example of a function where half-duplex communication complexity with adversary is strictly less than classical communication complexity.

Findings

Half-duplex protocols can outperform classical protocols in certain cases.

A specific function with lower half-duplex complexity was constructed.

This result shows a fundamental difference between the models.

Abstract

Half-duplex communication complexity with adversary was defined in [Hoover, K., Impagliazzo, R., Mihajlin, I., Smal, A. V. Half-Duplex Communication Complexity, ISAAC 2018.] Half-duplex communication protocols generalize classical protocols defined by Andrew Yao in [Yao, A. C.-C. Some Complexity Questions Related to Distributive Computing (Preliminary Report), STOC 1979]. It has been unknown so far whether the communication complexities defined by these models are different or not. In the present paper we answer this question: we exhibit a function whose half-duplex communication complexity with adversary is strictly less than its classical communication complexity.