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

Rahul Jain, Hartmut Klauck, Shengyu Zhang
2009 arXiv   pre-print
We show lower bounds of Ω(√(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 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.
arXiv:0908.4453v1 fatcat:mhv43mywpjdz7clfnrmnpbdi4e