Globally optimal diagnosis in systems with random faults

We consider probabilistic diagnosis in multiprocessor systems. Processors can test one another; fault-free processors give correct test results, while faulty testers are unpredictable. 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. A diagnosis algorithm is globally optimal if it has the highest probability of correctness among all (deterministic) diagnosis algorithms. We give fast globally optimal diagnosis algorithms for a class of test assignments including complete directed graphs and directed acyclic graphs. This is the first time that globally optimal diagnosis is given in a probabilistic model without any assumptions on the behavior of faulty processors.