On the Time-Complexity of Robust and Amnesic Storage

We consider wait-free implementations of a regular read/ write register for unauthenticated data using a collection of 3t + k base objects, t of which can be subject to Byzantine failures. We focus on amnesic algorithms that store only a limited number of values in the base objects. In contrast, non-amnesic algorithms store an unbounded number of values, which can eventually lead to problems of space exhaustion. Lower bounds on the time-complexity of read and write operations are currently met only by non-amnesic algorithms. In this paper, we show for the first time that amnesic algorithms can also meet these lower bounds. We do this by giving two amnesic constructions: for k = 1, we show that the lower bound of two communication rounds is also sufficient for every read operation to complete and for k = t + 1 we show that the lower bound of one round is also sufficient for every operation to complete.