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The advent of microprocessors as low-cost general- purpose computing elements has made feasible the implementation of multiprocessor systems containing a large number of cooperating modules. When the number of modules in the system is large it is unlikely that all of them are busy with computation at all times. Therefore, it may be possible to utilize this "slack" by having the nonbusy modules perform diagnostics. In this way computation and diagnosis are performed concurrently in real time. In this correspondence we consider the problem of designing systems in which concurrent computation/diagnosis is possible and we evaluate the potential of such approach.