Dynamic Observers for the Synthesis of Opaque Systems

  • Authors:
  • Franck Cassez;Jérémy Dubreil;Hervé Marchand

  • Affiliations:
  • National ICT Australia & CNRS, Sydney, Australia;INRIA Rennes - Bretagne Atlantique, Rennes, France;INRIA Rennes - Bretagne Atlantique, Rennes, France

  • Venue:
  • ATVA '09 Proceedings of the 7th International Symposium on Automated Technology for Verification and Analysis
  • Year:
  • 2009

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Abstract

In this paper, we address the problem of synthesizing opaque systems by selecting the set of observable events. We first investigate the case of static observability where the set of observable events is fixed a priori. In this context, we show that checking whether a system is opaque and computing an optimal static observer ensuring opacity are both PSPACE-complete problems. Next, we introduce dynamic partial observability where the set of observable events can change over time. We show how to check that a system is opaque w.r.t. a dynamic observer and also address the corresponding synthesis problem: given a system G and secret states S , compute the set of dynamic observers under which S is opaque. Our main result is that the synthesis problem can be solved in EXPTIME.