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Diagnosability of repairable faults

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Abstract

The diagnosis problem for discrete event systems consists in deciding whether some fault event occurred or not in the system, given partial observations on the run of that system. Diagnosability checks whether a correct diagnosis can be issued in bounded time after a fault, for all faulty runs of that system. This problem appeared two decades ago and numerous facets of it have been explored, mostly for permanent faults. It is known for example that diagnosability of a system can be checked in polynomial time, while the construction of a diagnoser is exponential. The present paper examines the case of transient faults, that can appear and be repaired. Diagnosability in this setting means that the occurrence of a fault should always be detected in bounded time, but also before the fault is repaired, in order to prepare for the detection of the next fault or to take corrective measures while they are needed. Checking this notion of diagnosability is proved to be PSPACE-complete. It is also shown that faults can be reliably counted provided the system is diagnosable for faults and for repairs.

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Notes

  1. Alternatively, we can define L(A) as words that terminate with a letter of Σ o , or equivalently by assuming faulty states in A that can only be reached by visible transitions, which does not reduce the generality of the setting.

  2. where N O,U F,V a n have the same meaning as in the automaton VA.

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Acknowledgements

The authors would like to thank Francois Godi, Xavier Montillet and Chen Qian, master students at ENS Rennes, for interesting discussions that led to this work.

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Authors and Affiliations

  1. INRIA Rennes, Campus de Beaulieu, 35042, Rennes cedex, France

    Eric Fabre, Loïc Hélouët & Hervé Marchand

  2. ENS Cachan, 61 Avenue du Président Wilson, 94230, Cachan, France

    Engel Lefaucheux

Authors
  1. Eric Fabre
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  2. Loïc Hélouët
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  3. Engel Lefaucheux
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  4. Hervé Marchand
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Corresponding author

Correspondence to Eric Fabre.

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This article belongs to the Topical Collection: Special Issue on Diagnosis, Opacity and Supervisory Control of Discrete Event Systems

Guest Editors: Christos G. Cassandras and Alessandro Giua

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Fabre, E., Hélouët, L., Lefaucheux, E. et al. Diagnosability of repairable faults. Discrete Event Dyn Syst 28, 183–213 (2018). https://doi.org/10.1007/s10626-017-0255-8

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  • DOI: https://doi.org/10.1007/s10626-017-0255-8

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