On Verification of Strong Periodic D-Detectability for Discrete Event Systems

Abstract

Detectability has been introduced as a generalization of state-estimation properties of discrete event systems studied in the literature. It asks whether the current and subsequent states of a system can be determined based on observations. Since, in some applications, to exactly determine the current and subsequent states may be too strict, a relaxed notion of D-detectability has been introduced, distinguishing only certain pairs of states rather than all states. Four variants of D-detectability have been 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 actually NL-complete). However, to the best of our knowledge, it is an open problem whether there exists a polynomial-time algorithm deciding strong periodic D-detectability. We solve this problem by showing that deciding strong periodic D-detectability is a PSpace-complete problem, and hence there is no polynomial-time algorithm unless PSpace = P. We further show that there is no polynomial-time algorithm deciding strong periodic D-detectability 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

IGA PrF 2022 018

Martin Trnečka
Jiří Balun, Jiří Valůšek

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

WODES, 263-268, 2020
Discrete-Event Systems and Theoretical Computer Science Research Group

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