Catastrophic Faults in Reconfigurable Linear Arrays of Processors

In regular architectures of identical processing elements, a widely used technique to improve the reconfigurability of the system consists of providing redundant processing elements and mechanisms of reconfiguration. In this paper we consider linear arrays of processing elements, with unidirectional bypass links of length g. We count the number of particular sets of faulty processing elements. We show that the number of catastrophic faults of g elements is equal to the (g-1)-th Catalan number. We also provide algorithms to rank and unrank all catastrophic sets of g faults. Finally, we describe a linear time algorithm that generate all such sets of faults