Closure and Convergence: A Foundation of Fault-Tolerant Computing

We give a formal de nition of what it means for a system to \tolerate" a class of \faults". The de nition consists of two conditions: One, if a fault occurs when the system state is within a set of \legal" states, the resulting state is within some larger set and, if faults continue occurring, the system state remains within that larger set (Closure). And two, if faults stop occurring, the system eventually reaches a state within the legal set (Convergence). We demonstrate the applicability of our de nition for specifying and verifying the fault-tolerance properties of a variety of digital and computer systems. Further, using the de nition, we obtain a simple classi cation of fault-tolerant systems and discuss methods for their systematic design.