Simulating Few by Many: k-Concurrency via k-Set Consensus

We introduce a new novel emulation by which we show an equivalence between k-Set Consensus and k-concurrency: Any number of processors when given k-Set Consensus can solve wait-free (read-write), any task which can be solved wait-free read-write when concurrency is limited to k, and visa versa. As a result of showing the models equivalent we obtain a generalization of Herlihy’s Universality result: Processors using k-Set Consensus can implement k independent arbitrary object, with a progress guaranteed on at least one of the objects. Similarly, we obtain a new proof that n processors with k-Set Consensus can rename into n + (k − 1) slots. We obtain these results as they are easily derived for the model when concurrency is limited to k.