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Conference Papers Year : 2016

Accurate approximate diagnosability of stochastic systems

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 ε-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 decid-ability status of the diagnosability problems: (uniform) ε-diagnosability and uniform AA-diagnosability are undecidable while AA-diagnosability is decidable in PTIME, answering a longstanding open question.
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Dates and versions

hal-01220954 , version 1 (28-10-2015)
hal-01220954 , version 2 (07-12-2015)

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  • HAL Id : hal-01220954 , version 2

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Nathalie Bertrand, Serge Haddad, Engel Lefaucheux. Accurate approximate diagnosability of stochastic systems. 10th International Conference on Language and Automata Theory and Applications, Mar 2016, Prague, Czech Republic. ⟨hal-01220954v2⟩
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