A characterization of t/s-diagnosability and sequential t-diagnosability in designs

A multiprocessing system is t/s-diagnosable if all faulty processors can be identified to within s processors, provided there are no more than t faulty processors. A characterization theorem of S. Karunanithi and A.D. Friedman (1979) for t/s-diagnosability in certain special cases of systems called designs is extended to the entire class of D_1,t´ (n) designs. It is shown that for large t, s is approximately t²/4t´. Furthermore, the minimum number of processors needed to attain a given diagnosability is derived. A multiprocessor system is sequentially t-diagnosable if at least one faulty processor can be identified provided there are no more than t faulty processors. A theorem by F. Preparata, G. Metze, and R. Chien (1967), giving a sufficient condition for sequential t-diagnosability in the single-loop system (a special case of designs), is extended to the entire class of D_1,t´(n) designs. It is shown that, for large t, approximately t²/4t´ nodes are needed for a D_1,t´ (n) design to be sequentially t-diagnosable