Depth-Independent Lower bounds on the Communication Complexity of Read-Once Boolean Formulas

Rahul Jain; Hartmut Klauck; Shengyu Zhang

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arXiv · 0908.4453

Depth-Independent Lower bounds on the Communication Complexity of Read-Once Boolean Formulas

Rahul Jain·Hartmut Klauck·Shengyu Zhang

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Abstract

We show lower bounds of $Ω(\sqrt{n})$ and $Ω(n^{1/4})$ on the randomized and quantum communication complexity, respectively, of all $n$-variable read-once Boolean formulas. Our results complement the recent lower bound of $Ω(n/8^d)$ by Leonardos and Saks and $Ω(n/2^{Ω(d\log d)})$ by Jayram, Kopparty and Raghavendra for randomized communication complexity of read-once Boolean formulas with depth $d$. We obtain our result by "embedding" either the Disjointness problem or its complement in any given read-once Boolean formula.

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BibTeX RIS

Rahul Jain, Hartmut Klauck, Shengyu Zhang. 2009-08-31. Depth-Independent Lower bounds on the Communication Complexity of Read-Once Boolean Formulas. https://arxiv.org/abs/0908.4453

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