Dynamic Observers for the Synthesis of Opaque Systems

Franck Cassez (1) , Jérémy Dubreil (2) , Hervé Marchand (2)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 VERTECS - Verification models and techniques applied to testing and control of reactive systems

In this paper, we address the problem of synthesizing opaque systems. A secret predicate S over the runs of a system G is opaque to an external user having partial observability over G, if s/he can never infer from the observation of a run of G that the run belongs to S. We first investigate the case of static partial observability where the set of events the user can observe is fixed a priori. In this context, we show that checking whether a system is opaque is PSPACE-complete, which implies that computing an optimal static observer ensuring opacity is also a PSPACE-complete problem. Next, we introduce dynamic partial observability where the set of events the user can observe changes over time. We show how to check that a system is opaque w.r.t. to 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 set of such observers can be finitely represented and can be computed in EXPTIME.

Domaines: Calcul formel [cs.SC]

Franck Cassez, Jérémy Dubreil, Hervé Marchand. Dynamic Observers for the Synthesis of Opaque Systems. 7th International Symposium on Automated Technology for Verification and Analysis (ATVA'09), Oct 2009, Macao SAR, China. pp.352-367, ⟨10.1007/978-3-642-04761-9_26⟩. ⟨inria-00399229⟩