Abstract
We present a tight tradeoff between the expected communication complexity C (for a two-processor system) and the number R of random bits used by any Las Vegas protocol for the list-nondisjointness function of two lists of n numbers of n bits each. This function evaluates to 1 if and only if the two lists correspond in at least one position. We show a log( n 2 / C ) lower bound on the number of random bits used by any Las Vegas protocol, Ω ( n ) ≤ C ≤ O ( n 2 ). We also show that expected communication complexity C , Ω ( n log n ) ≤ C ≤ O ( n 2 ), can be achieved using no more than log( n 2 / C ) + ⌈log(2 + log( n 2 / C ))⌉ + 6 random bits.
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