Many problems in the area of symbolic computing can be solved by iterative algorithms. Implementations of these algorithms on multiprocessors can be synchronous or asynchronous. Asynchronous implementations are potentially more efficient because synchronization is a major source of performance degradation in most multiprocessor systems. In this paper, sufficient conditions for the convergence of asynchronous iterations to desired solutions are given. The main sufficient condition is shown to be also necessary for the case of finite data domains. The results are applied to prove the convergence of three asynchronous algorithms for the all-pairs shortest path problem, the consistent labeling problem, and a neural net model.
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