State space generation for degradable multiprocessor systems

Degradable multiprocessors can have a large number of different structural configurations (states) after being altered by faults. Many such states may be equivalent relative to their overall effect on a system's ability to perform. Hence, depending on the performability measure, the number of states can often be reduced to a much smaller set of representative configurations, one for each equivalence class. An algorithm that generates these representatives and determines the size of each equivalence class is presented. The algorithm assumes that performance is invariant under structural symmetries and thus employs a symmetry permutation group. The information so obtained permits construction of a stochastic process model that supports the performability measure in question. The group-theoretic concepts on which the algorithm is based are presented, and its complexity is considered. The use of the algorithm to construct a performability model is illustrated, and possible extensions are addressed.<>