Question: [34] In Theorem 6.11.1 it was shown that for a deterministic protocol of say, complexity O(1), to compute the identity function Alice and Bob need

[34] In Theorem 6.11.1 it was shown that for a deterministic protocol of say, complexity O(1), to compute the identity function Alice and Bob need to exchange about C(y) bits, even if the required information C(y|x) is much less than C(y). Show that for randomized protocols the communication complexity is close to C(y|x).

Comments. Source: [H.M. Buhrman, M. Kouck´y, and N.K. Vereshchagin, Proc. 23rd IEEE Conf. Comput. Complexity, 2008, pp. 321–331].

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