On Verification of D-Detectability for Discrete Event Systems

Abstract

Detectability is a state-estimation property asking whether the current and subsequent states of a system can be determined based on observations. To exactly determine the current and subsequent states may be, however, too strict in some applications. Therefore, Shu and Lin relaxed detectability to D-detectability distinguishing only certain pairs of states rather than all states. Four variants of D-detectability were defined: strong (periodic) D-detectability and weak (periodic) D-detectability. Deciding weak (periodic) D-detectability is PSpace-complete, while deciding strong (periodic) detectability or strong D-detectability is polynomial, and we show that it is NL-complete. To the best of our knowledge, it is an open problem whether there exists a polynomial-time algorithm deciding strong periodic D-detectability. We show that deciding strong periodic D-detectability is a PSpace-complete problem, which means that there is no polynomial-time algorithm, unless every problem solvable in polynomial space can be solved in polynomial time. We further show that there is no polynomial-time algorithm even for systems with a single observable event, unless P = NP. Finally, we propose a class of systems for which the problem is tractable.

Projects

Verification and Control of Networked Discrete Event Systems

Tomáš Masopust, Jan Komenda
Jiří Balun, Stéphane Lafortune, Spyros Reveliotis, Feng Lin

Authors

Jiří Balun
Tomáš Masopust

Automatica 133, 2021
Discrete-Event Systems and Theoretical Computer Science Research Group
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