Tamper-tolerant diagnosability analysis and tampering detectability in discrete event systems under cost constraints

This paper addresses fault diagnosis and tampering detection in discrete event systems modeled with nondeterministic finite automata under malicious attacks. We propose a novel structure to simultaneously track the occurrence of fault events and tampering actions in systems compromised by attacks (i.e., by arbitrary deletions, insertions, or substitutions of observed symbols). Assuming that each deletion, insertion, or substitution bears a positive cost to the attacker, two scenarios are taken into account: (1) a bounded number of attacks or, more generally, a total cost constraint on tampering actions, and (2) an unbounded number of attacks or, more generally, no constraints on the total cost of tampering actions. Several examples are presented to demonstrate the influence of cost constraints on tamper-tolerant diagnosis and tampering detection. A state isolation technique is developed to deal with the fault and/or tampering action detection problem via an external observer that aims to isolate the estimated states within a certain subset of states based on a given sequence of observations. We also report a technique of polynomial complexity for verifying tamper-tolerant diagnosability and tampering detectability.