Abstract
Diagnosis of multiprocessor systems in which faulty processors can be replaced by spares or repaired is known as sequential diagnosis. A generalization is considered of classical sequential diagnosis, referred to as diagnosis and repair, under a probabilistic model for the faults and test outcomes in a system. It is shown that correct diagnosis and repair of all faulty processors can be achieved with high probability in a large class of systems including, for example, rings, grids, meshes, tori, and hypercubes. These results show, without restrictive assumptions on the behavior of faulty processors, that correct diagnosis can be achieved in these widely used, low-degree systems when a fixed percentage of the processors in the system are faulty.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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