We introduce a new model of partial synchrony for read-write shared memory systems. This model is based on the notion of set timeliness—a natural and straightforward generalization of the seminal concept of timeliness in the partially synchrony model of Dwork, Lynch and Stockmeyer . Despite its simplicity, the concept of set timeliness is powerful enough to define a family of partially synchronous systems that closely match individual instances of the t-resilient k-set agreement problem among n processes, henceforth denoted (t, k, n) agreement. In particular, we use it to give a partially synchronous system that is is synchronous enough for solving (t, k, n) agreement, but not enough for solving two incrementally stronger problems, namely, (t + 1, k, n)-agreement, which has a slightly stronger resiliency requirement, and (t, k − 1, n)-agreement, which has a slightly stronger agreement requirement. This is the first partially synchronous system that separates between these sub-consensus problems. The above results show that set timeliness can be used to study and compare the partial synchrony requirements of problems that are strictly weaker than consensus.
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