An XOR Lemma for Deterministic Communication Complexity

Siddharth Iyer; Anup Rao

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arXiv · 2407.01802

An XOR Lemma for Deterministic Communication Complexity

Siddharth Iyer·Anup Rao

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Abstract

We prove a lower bound on the communication complexity of computing the $n$-fold xor of an arbitrary function $f$, in terms of the communication complexity and rank of $f$. We prove that $D(f^{\oplus n}) \geq n \cdot \Big(\frac{Ω(D(f))}{\log \mathsf{rk}(f)} -\log \mathsf{rk}(f)\Big )$, where here $D(f), D(f^{\oplus n})$ represent the deterministic communication complexity, and $\mathsf{rk}(f)$ is the rank of $f$. Our methods involve a new way to use information theory to reason about deterministic communication complexity.

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BibTeX RIS

Siddharth Iyer, Anup Rao. 2024-07-01. An XOR Lemma for Deterministic Communication Complexity. https://arxiv.org/abs/2407.01802

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