Detectability of labeled weighted weighted automata over monoids release_jiy4ti6invhafbb3l5r26rzfom

by Kuize Zhang

Released as a article .

2020  

Abstract

Discrete-event systems (DESs) are generally composed of transitions between discrete states caused by spontaneous occurrences of partially-observed (aka labeled) events. Detectability is a fundamental property in labeled dynamical systems, which describes whether one can use an observed label sequence to reconstruct the current state. Labeled weighted automata (LWAs) can be regarded as a timed model of DESs. In this paper, by developing appropriate methods, we for the first time obtain characterization of four fundamental notions of detectability for general LWAs over monoids, where the four notions are strong (periodic) detectability (SD and SPD) and weak (periodic) detectability (WD and WPD). The contributions of the current paper are as follows. Firstly, we formulate the notions of concurrent composition, observer, and detector for LWAs. Secondly, we use the concurrent composition to give an equivalent condition for SD, use the detector to give an equivalent condition for SPD, and use the observer to give equivalent conditions for WD and WPD, all for general LWAs. Thirdly, we prove that for an LWA over monoid (β„•,+,0) (denoted by π’œ^β„•), its concurrent composition, observer, and detector can be computed in NP, 2-EXPTIME, and NP, respectively, by developing a novel connection between π’œ^β„• and the NP-complete exact path length problem (proved by [NykΓ€nen and Ukkonen, 2002]). As a result, we prove that for π’œ^β„•, SD and SPD can be verified in coNP, while WD and WPD can be verified in 2-EXPTIME. Finally, we prove that the problems of verifying SD and SPD of deterministic π’œ^β„• are both coNP-hard. The original methods developed in this paper will provide foundations for characterizing other fundamental properties (e.g., diagnosability and opacity) in LWAs over monoids.
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Date   2020-12-02
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arXiv  2006.14164v2
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