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WAIT-FREE k-SET AGREEMENT IS IMPOSSIBLE: THE TOPOLOGY OF PUBLIC KNOWLEDGE∗March 14th, 2000
Abstract. In the classical consensus problem, each of n processors receives a private input value and produces a decision value which is one of the original input values, with the requirement that all processors decide the same value. A central result in distributed computing is that, in several standard models including the asynchronous shared-memory model, this problem has no determinis- tic solution. The k-set agreement problem is a generalization of the classical consensus proposed by Chaudhuri [Inform. and Comput., 105 (1993), pp. 132–158], where the agreement condition is weak- ened so that the decision values produced may be different, as long as the number of distinct values is at most k. For n > k 2 it was not known whether this problem is solvable deterministically in the asynchronous shared memory model. In this paper, we resolve this question by showing that for any k < n, there is no deterministic wait-free protocol for n processors that solves the k-set agreement problem.
