An improved testing scheme for catastrophic fault patterns

In a linear array of processors, a single faulty element in any location is sufficient to stop the flow of information from one side to the other. A common approach for achieving fault tolerance in such systems is through the incorporation of redundant links in a regular fashion. These links (called bypass links) can be activated in a reconfiguration phase to bypass faulty elements. There are some inherent limits in this approach. In particular, there are sets of faults occurring in strategic locations which affect the entire system in an unrepairable way, regardless of the amount of redundancy, and cannot be overcome by any clever reconfiguration process, see [7]. These sets of faults are called Catastrophic Fault Patterns (CFP) and have been extensively studied in the literature [1,2,4–6,8, 10]. The rather intuitive guess that any cut set is a CFP is unfortunately incorrect; on the contrary, they have a rather interesting structure with non-trivial symmetries