Bounded Predictability for Faulty Discrete Event Systems

A discrete event system that is predictable can anticipate faults and act accordingly. However, bare predictability (as found in the literature) has some drawbacks. One does not know exactly when a fault occurs (it could be immediately or long after it is predicted). We propose lower and upper bound refinements of predictability, called (Ib, ub)-predictability. A lower bound guarantees a fault to occur after certain execution steps, whereas an upper bound guarantees a fault to occur, in the future, but before some steps. This information can be exploited by the system to adopt the best contingency plan. We formally define the notions of lb-predictability and ub-predictability, present a decision algorithm to verify it on arbitrary systems, and illustrate them with examples.