Note: [*] This work was partially supported by the Alexander von Humboldt Foundation.
Abstract: The state detection problem and fault diagnosis/prediction problem are fundamental topics in many areas. In this paper, we consider discrete-event systems (DESs) modeled by finite-state automata (FSAs). There exist plenty of results on decentralized versions of the latter problem but there is almost no result for a decentralized version of the former problem. In this paper, we propose a decentralized version of strong detectability called co-detectability which means that if a system satisfies this property, for each generated infinite-length event sequence, in at least one location the current and subsequent states can be determined by observations in the location after a common observation time delay. We prove that the problem of verifying co-detectability of deterministic FSAs is coNP-hard. Moreover, we use a unified concurrent-composition method to give PSPACE verification algorithms for co-detectability, co-diagnosability, and co-predictability of FSAs, without any assumption on or modification of the FSAs under consideration, where co-diagnosability is first studied by [Debouk & Lafortune & Teneketzis 2000], co-predictability is first studied by [Kumar & Takai 2010]. By our proposed unified method, one can see that in order to verify co-detectability, more technical difficulties will be met compared with verifying the other two properties, because in co-detectability, generated outputs are counted, but in the latter two properties, only occurrences of events are counted. For example, when one output was generated, any number of unobservable events could have occurred. PSPACE-hardness of verifying co-diagnosability is already known in the literature. In this paper, we prove PSPACE-hardness of verifying co-predictability.
