Section: New Results

Control synthesis

Synthesis of opaque systems

Participant : Hervé Marchand.

Opacity is a security property formalizing the absence of (secret) information leakage. 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 he can never infer from the observation of a run of G that the run belongs to S. We choose to control the observability of events by adding a device, called a mask, between the system G and the users. We first investigate the case of static partial observability where the set of events the user can observe is fixed once and for all by a static mask. In this context, we show that checking whether a system is opaque is PSPACE-complete, which implies that computing an optimal static mask 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 and is determined by a dynamic mask. We show how to check that a system is opaque w.r.t. to a dynamic mask and also address the corresponding synthesis problem: given a system G and secret states S, compute the set of dynamic masks under which S is opaque. Our main result is that the set of such masks can be finitely represented and can be computed in EXPTIME and that this is a lower bound. We also address the problem of computing an optimal mask. This work was published in FMSD [9] .

Symbolic Supervisory Control of Infinite Transition Systems under Partial Observation using Abstract Interpretation

Participant : Hervé Marchand.

In the DEDS article [12] , we propose algorithms for the synthesis of state-feedback controllers with partial observation of infinite state discrete event systems modelled by Symbolic Transition Systems. We provide models of safe memoryless controllers both for potentially deadlocking and for deadlock free controlled systems. The termination of the algorithms solving these problems is ensured using abstract interpretation techniques which provide an overapproximation of the transitions to disable. We then extend our algorithms to controllers with memory and to online controllers. We also propose improvements in the synthesis of controllers in the finite case which, to our knowledge, provide more permissive solutions than previously proposed in the literature. Our tool SMACS gives an empirical validation of our methods by showing their feasibility, usability and efficiency.

Playing optimally on timed automata with random delays

Participant : Nathalie Bertrand.

In [15] , we marry continuous time Markov decision processes (CTMDPs) with stochastic timed automata into a model with joint expressive power. This extension is very natural, as the two original models already share exponentially distributed sojourn times in locations. It enriches CTMDPs with timing constraints, or symmetrically, stochastic timed automata with one conscious player. Our model maintains the existence of optimal control known for CTMDPs. This also holds for a richer model with two players, which extends continuous time Markov games. But we have to sacrifice the existence of simple schedulers: polyhedral regions are insufficient to obtain optimal control even in the single-player case.