An XOR Lemma for Deterministic Communication Complexity
<|reference_start|>An XOR Lemma for Deterministic Communication Complexity: 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 $D(f^{\oplus n}) \geq n \cdot \Big(\frac{\Omega(D(f))}{\log \mathsf{rk}(f)} -\log \mathsf{rk}(f)\Big )$, 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.<|reference_end|>
@article{iyer2024an,
    title={An XOR Lemma for Deterministic Communication Complexity},
    author={Siddharth Iyer and Anup Rao},
    journal={arXiv preprint arXiv:2407.01802},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.01802},
    primaryClass={cs.CC}
}