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Discrete Event Dynamic Systems

, Volume 28, Issue 1, pp 83–108 | Cite as

Opacity for linear constraint Markov chains

  • Béatrice Bérard
  • Olga Kouchnarenko
  • John MullinsEmail author
  • Mathieu Sassolas
Article
  • 139 Downloads
Part of the following topical collections:
  1. Special Issue on Performance Analysis and Optimization of Discrete Event Systems

Abstract

On a partially observed system, a secret φ is opaque if an observer cannot ascertain that its trace belongs to φ. We consider specifications given as Constraint Markov Chains (CMC), which are underspecified Markov chains where probabilities on edges are required to belong to some set. The nondeterminism is resolved by a scheduler, and opacity on this model is defined as a worst case measure over all implementations obtained by scheduling. This measures the information obtained by a passive observer when the system is controlled by the smartest scheduler in coalition with the observer. When restricting to the subclass of Linear CMC, we compute (or approximate) this measure and prove that refinement of a specification can only improve opacity.

Keywords

Opacity Markov models Specification Refinement 

Notes

Acknowledgments

Partially supported by a grant from Coopération France-Québec, Service Coopération et Action Culturelle 2012/26/SCAC (French Government), the NSERC Discovery Individual grant No. 13321 (Government of Canada), the FQRNT Team grant No. 167440 (Quebec’s Government) and the CFQCU France-Quebec Cooperative grant No. 167671 (Quebec’s Government). This research has been partially performed while the third author was visiting the LIP6, Université Pierre & Marie Curie.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Sorbonne UniversitéParisFrance
  2. 2.INRIA and LSV, CNRS and ENS CachanUniversité Paris-SaclaySaclayFrance
  3. 3.Université Bourgogne Franche-ComtéFEMTO-ST, CNRS UMR 6174BesançonFrance
  4. 4.Department of Computer & Software EngineeringÉcole Polytechnique de MontréalMontrealCanada
  5. 5.Université Paris-Est, LACLCréteilFrance

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