On the cost of diagnosis with disambiguation

Abstract

Diagnosis consists in deciding from a partial observation of a system whether a fault has occurred. A system is diagnosable if there exists a mechanism (a diagnoser) that accurately detects faults a finite number of steps after their occurrence. In a regular setting, a diagnoser builds an estimation of possible states of the system after an observation to decide if a fault has occurred. This paper addresses diagnosability (deciding whether a system is diagnosable) and its cost for safe Petri nets. We define an energy-like cost model for Petri nets: transitions can consume or restore energy of the system. We then give a partial order representation for state estimation, and extend the cost model and the capacities of diagnosers. Diagnosers are allowed to use additional energy to refine their estimations. In this setting, diagnosability is an energy game, and checking diagnosability under energy constraints is in 2-EXPTIME.