System diagnosis with smallest risk of error

Abstract

We consider the problem of fault diagnosis in multiprocessor systems. Every processor can test its neighbors; fault-free processors correctly identify the fault status of tested neighbors, while faulty testers can give arbitrary test results. Processors fail independently with constant probability p < 1/2 and the goal is to identify correctly the status of all processors, based on the set of test results. We give fast diagnosis algorithms with the highest possible probability of correctness for systems represented by complete bipartite graphs and by simple paths. This is for the first time that the most reliable fault diagnosis is given for these systems in a probabilistic model without any assumptions on the behavior of faulty processors.