Three results on interactive communication

7] A. Orlitsky. Worst-case interactive communication II: Two messages are not optimal. 11] H. Witsenhausen. The zero-error side information problem and chromatic numbers. 14] J. Friedman. Constructing o(n log n) size monotone formula for the kth threshold function on n variables. A m be determined for m 3? For one-way amortized complexity, let (k) be the chromatic number of G (k) , then ^ A 1 = lim k!1 1 k log (k) : Hence results on the chromatic number of strong direct products of graphs translate directly to results on amortized complexity. Witsenhausen 11] showed that when the characteristic hypergraph is the pentagon graph, ^ C 1 = 2 while ^ A 1 = 1 2 log 5. Feder, Kushilevitz, and Naor 10] applied results of Linial and Vazirani 17] on the chromatic numbers of strong direct products of graphs to obtain bounds on a related problem. What about ^ A 2 and ^ A 3 ? Result 2 can be reened to include , the number of P Y 's ambiguity sets deened in Equation (5): ^ C 2 log log + 2 log ^