TR24-111 Authors: Siddharth Iyer, Anup Rao

Publication: 1st July 2024 21:59

Downloads: 327

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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 $D(f^{\oplus n}) \geq n \cdot \Big(\frac{\Omega(D(f))}{\log rk(f)} -\log rk(f)\Big )$, where here $D(f), D(f^{\oplus n})$ represent the deterministic communication complexity, and $rk(f)$ is the rank of $f$. Our methods involve a new way to use information theory to reason about deterministic communication complexity.