Conditional local self-regulation rules and a diagnostic algorithm for a multiprocessor system with circulant diagnostic structure based on these rules

We consider local testing on the system level for multiprocessor (modular) computational systems (CS) with multiple faults. CS has a circulant diagnostic structure. Outcomes of the tests performed by faulty units correspond to a well-known model of Preparata, Metze, and Chien. The testing problem is formulated as the problem of finding at least one actually operational unit with which one can diagnose the state of the system as a whole. We introduce the conditions for finding a set of units that includes all faulty units present in the system. We present a system self-testing algorithm. We show that using this algorithm, one can reach local $t$-diagnosability of a CS with circulant diagnostic structure for any number of units $N$ and fault multiplicity $t$ that satisfy $N\geq2t+1$.