Trading information complexity for error

We consider the standard two-party communication model. The central problem studied in this article is how much one can save in information complexity by allowing an error of ε. • For arbitrary functions, we obtain√ lower bounds and upper bounds indicating a gain that is of order Ω(h(ε)) and O(h( ε)), respectively. Here h denotes the binary entropy function. • We analyze the case of the two-bit AND function in detail to show that for this function the gain is Θ(h(ε)). This answers a question of Braverman et al. (STOC’13). • We obtain sharp bounds for the set disjointness function of order n. For the √case of the distributional error, we introduce a new protocol that achieves a gain of Θ( h(ε)) provided that n is sufficiently large. We apply these results to answer another question of Braverman et al. regarding the randomized communication complexity of the set disjointness function.