Average and Randomized Communication Complexity

42 and transmits the index of the set that contains x. By the model assumption he doesn't need to transmit which partition was picked. P Y then, transmits 1 if y belongs to the same set in the partition and 0 otherwise. The number of bits transmitted is 1 + dlog n b1+2(n?1)c e. The error probability is clearly 0 if x = y and, by symmetry or a more cumbersome argument, at most 2 for x 6 = y. As mentioned before, the protocol relies heavily on the assumption that the random experiment is shared by P X and P Y. There are far more than n partitions of f0; ::; n?1g into sets of size 1 + 2(n ? 1). Thus, if P X has to specify which one he uses, more than log n + 1 bits must be transmitted. In fact, it is stated in 2] that under the separation of random sources assumption, ^ C R (equ; ^) = (log log n). We note that for the equality function worst case and average errors yield similar complexities.