coping with Delays and Time-Outs in Binary Search Procedures

How many questions are necessary to guess an unknown number x in the set S = {1, 2, ..., n}, by using only comparison questions, that is questions of the type "Is x ≤ a?", when answers are received with a constant delay d, and up to a constant number c of the answers can be lost, i.e. can be not received at all? We exactly solve this problem for all integers d ≥ 0 and c = 1. We also briefly discuss the analogy between the above problem and that of broadcasting over a fully connected network with link latency.

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