Simulation relations for fault-tolerance

We present a formal characterization of fault-tolerant behaviors of computing systems via simulation relations. This formalization makes use of variations of standard simulation relations in order to compare the executions of a system that exhibits faults with executions where no faults occur; intuitively, the latter can be understood as a specification of the system and the former as a fault-tolerant implementation. By employing variations of standard simulation algorithms, our characterization enables us to algorithmically check fault-tolerance in polynomial time, i.e., to verify that a system behaves in an acceptable way even subject to the occurrence of faults. Furthermore, the use of simulation relations in this setting allows us to distinguish between the different levels of fault-tolerance exhibited by systems during their execution. We prove that each kind of simulation relation preserves a corresponding class of temporal properties expressed in CTL; more precisely, masking fault-tolerance preserves liveness and safety properties, nonmasking fault-tolerance preserves liveness properties, while failsafe fault-tolerance guarantees the preservation of safety properties. We illustrate the suitability of this formal framework through its application to standard examples of fault-tolerance.