Almost certain fault diagnosis through algorithm-based fault tolerance

Algorithm-based fault tolerance has been proposed as a technique to detect incorrect computations in multiprocessor systems. In algorithm-based fault tolerance, processors produce data elements that are checked by concurrent error detection mechanisms. We investigate the efficacy of this approach for diagnosis of processor faults. Because checks are performed on data elements, the problem of location of data errors must first be solved. We propose a probabilistic model for the faults and errors in a multiprocessor system and use it to evaluate the probabilities of correct error location and fault diagnosis. We investigate the number of checks that are necessary to guarantee error location with high probability. We also give specific check assignments that accomplish this goal. We then consider the problem of fault diagnosis when the locations of erroneous data elements are known. Previous work on fault diagnosis required that the data sets produced by different processors be disjoint. We show, for the first time, that fault diagnosis is possible with high probability, even in systems where processors combine to produce individual data elements