On the Communication Complexity of Read-Once AC^0 Formulae

Abstract--We study the 2-party randomized communication complexity of read-once AC0 formulae. For balanced AND-OR trees T with n inputs and depth d, we show that the communication complexity of the function fT (x, y) = T(xy) is (n/4d ) where (xy)i is defined so that the resulting tree also has alternating levels of AND and OR gates. For each bit of x, y, the operation is either AND or OR depending on the gate in T to which it is an input. Using this, we show that for general AND-OR trees T with n inputs and depth d, the communication complexity of fT (x, y) is n/2(d log d) . These results generalize the classical results on the communication complexity of setdisjointness [1], [2] (where T is an OR -gate) and recent results on the communication complexity of the TRIBES functions [3] (where T is a depth-2 read-once formula). Our techniques build on and extend the information complexity methodology [4], [5], [3] for proving lower bounds on randomized communication complexity. Our analysi...

• Type: Conference
• Year: 2009
• Where: COCO
• Authors: T. S. Jayram, Swastik Kopparty, Prasad Raghavendra
• Keywords: Algorithms, AND-OR Trees, COCO 2009, Communication Complexity, Information Complexity