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bertrand:hal-01220954

N. Bertrand, S. Haddad, E. Lefaucheux. Accurate approximate diagnosability of stochastic systems. In 10th International Conference on Language and Automata Theory and Applications, Prague, Czech Republic, March 2016.

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Abstract

Diagnosis of partially observable stochastic systems prone to faults was introduced in the late nineties. Diagnosability, i.e. the existence of a diagnoser, may be specified in different ways: (1) exact diag-nosability (called A-diagnosability) requires that almost surely a fault is detected and that no fault is erroneously claimed while (2) approximate diagnosability (called epsilon-diagnosability) allows a small probability of error when claiming a fault and (3) accurate approximate diagnosability (called AA-diagnosability) requires that this error threshold may be chosen arbitrarily small. Here we mainly focus on approximate diagnoses. We first refine the almost sure requirement about finite delay introducing a uniform version and showing that while it does not discriminate between the two versions of exact diagnosability this is no more the case in approximate diagnosis. Then we establish a complete picture for the decidability status of the diagnosability problems: (uniform) epsilon-diagnosability and uniform AA-diagnosability are undecidable while AA-diagnosability is decidable in PTIME, answering a longstanding open question

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Nathalie Bertrand http://www.irisa.fr/prive/nbertran/

BibTex Reference

@InProceedings{bertrand:hal-01220954,
   Author = {Bertrand, N. and Haddad, S. and Lefaucheux, E.},
   Title = {Accurate approximate diagnosability of stochastic systems},
   BookTitle = {10th International Conference on Language and Automata Theory and Applications},
   Publisher = {Springer},
   Address = {Prague, Czech Republic},
   Month = {March},
   Year = {2016}
}

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