Depth-Independent Lower Bounds on the Communication Complexity of Read-Once Boolean Formulas [chapter]

Rahul Jain, Hartmut Klauck, Shengyu Zhang
2010 Lecture Notes in Computer Science  
We show lower bounds of Ω( √ n) and Ω(n 1/4 ) on the randomized and quantum communication complexity, respectively, of all nvariable read-once Boolean formulas. Our results complement the recent lower bound of Ω(n/8 d ) by Leonardos and Saks [LS09] and Ω(n/2 O(d log d) ) by Jayram, Kopparty and Raghavendra [JKR09] 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.
doi:10.1007/978-3-642-14031-0_8 fatcat:zgw77zfaargctpdjunxxc7tf5q