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Foundation of Diagnosis and Predictability in Probabilistic Systems

Authors Nathalie Bertrand, Serge Haddad, Engel Lefaucheux



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Nathalie Bertrand
Serge Haddad
Engel Lefaucheux

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Nathalie Bertrand, Serge Haddad, and Engel Lefaucheux. Foundation of Diagnosis and Predictability in Probabilistic Systems. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 417-429, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)
https://doi.org/10.4230/LIPIcs.FSTTCS.2014.417

Abstract

In discrete event systems prone to unobservable faults, a diagnoser must eventually detect fault occurrences. The diagnosability problem consists in deciding whether such a diagnoser exists. Here we investigate diagnosis for probabilistic systems modelled by partially observed Markov chains also called probabilistic labeled transition systems (pLTS). First we study different specifications of diagnosability and establish their relations both in finite and infinite pLTS. Then we analyze the complexity of the diagnosability problem for finite pLTS: we show that the polynomial time procedure earlier proposed is erroneous and that in fact for all considered specifications, the problem is PSPACE-complete. We also establish tight bounds for the size of diagnosers. Afterwards we consider the dual notion of predictability which consists in predicting that in a safe run, a fault will eventually occur. Predictability is an easier problem than diagnosability: it is NLOGSPACE-complete. Yet the predictor synthesis is as hard as the diagnoser synthesis. Finally we introduce and study the more flexible notion of prediagnosability that generalizes predictability and diagnosability.
Keywords
  • Partially observed systems
  • Diagnosis
  • Markov chains

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References

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