Analysis of Non-Linear Probabilistic Hybrid Systems

This paper shows how to compute, for probabilistic hybrid systems, the clock approximation and linear phase-portrait approximation that have been proposed for non probabilistic processes by Henzinger et al. The techniques permit to define a rectangular probabilistic process from a non rectangular one, hence allowing the model-checking of any class of systems. Clock approximation, which applies under some restrictions, aims at replacing a non rectangular variable by a clock variable. Linear phase-approximation applies without restriction and yields an approximation that simulates the original process. The conditions that we need for probabilistic processes are the same as those for the classic case.Comment: In Proceedings QAPL 2011, arXiv:1107.074

Computing Distances between Probabilistic Automata

We present relaxed notions of simulation and bisimulation on Probabilistic Automata (PA), that allow some error epsilon. When epsilon is zero we retrieve the usual notions of bisimulation and simulation on PAs. We give logical characterisations of these notions by choosing suitable logics which differ from the elementary ones, L with negation and L without negation, by the modal operator. Using flow networks, we show how to compute the relations in PTIME. This allows the definition of an efficiently computable non-discounted distance between the states of a PA. A natural modification of this distance is introduced, to obtain a discounted distance, which weakens the influence of long term transitions. We compare our notions of distance to others previously defined and illustrate our approach on various examples. We also show that our distance is not expansive with respect to process algebra operators. Although L without negation is a suitable logic to characterise epsilon-(bi)simulation on deterministic PAs, it is not for general PAs; interestingly, we prove that it does characterise weaker notions, called a priori epsilon-(bi)simulation, which we prove to be NP-difficult to decide.Comment: In Proceedings QAPL 2011, arXiv:1107.074

La gestion des loisirs publics à Montréal : l'exemple du parc de l'île Sainte-Hélène, 1874-1914

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal

Bisimulation for Labelled Markov Processes

AbstractIn this paper we introduce a new class of labelled transition systems—labelled Markov processes— and define bisimulation for them. Labelled Markov processes are probabilistic labelled transition systems where the state space is not necessarily discrete. We assume that the state space is a certain type of common metric space called an analytic space. We show that our definition of probabilistic bisimulation generalizes the Larsen–Skou definition given for discrete systems. The formalism and mathematics is substantially different from the usual treatment of probabilistic process algebra. The main technical contribution of the paper is a logical characterization of probabilistic bisimulation. This study revealed some unexpected results, even for discrete probabilistic systems. •Bisimulation can be characterized by a very weak modal logic. The most striking feature is that one has no negation or any kind of negative proposition.•We do not need any finite branching assumption, yet there is no need of infinitary conjunction. We also show how to construct the maximal autobisimulation on a system. In the finite state case, this is just a state minimization construction. The proofs that we give are of an entirely different character than the typical proofs of these results. They use quite subtle facts about analytic spaces and appear, at first sight, to be entirely nonconstructive. Yet one can give an algorithm for deciding bisimilarity of finite state systems which constructs a formula that witnesses the failure of bisimulation

Bisimulation and cocongruence for probabilistic systems

International audienc

Approximate reasoning for real-time probabilistic processes

We develop a pseudo-metric analogue of bisimulation for generalized semi-Markov processes. The kernel of this pseudo-metric corresponds to bisimulation; thus we have extended bisimulation for continuous-time probabilistic processes to a much broader class of distributions than exponential distributions. This pseudo-metric gives a useful handle on approximate reasoning in the presence of numerical information -- such as probabilities and time -- in the model. We give a fixed point characterization of the pseudo-metric. This makes available coinductive reasoning principles for reasoning about distances. We demonstrate that our approach is insensitive to potentially ad hoc articulations of distance by showing that it is intrinsic to an underlying uniformity. We provide a logical characterization of this uniformity using a real-valued modal logic. We show that several quantitative properties of interest are continuous with respect to the pseudo-metric. Thus, if two processes are metrically close, then observable quantitative properties of interest are indeed close.Comment: Preliminary version appeared in QEST 0

A progress-sensitive flow-sensitive inlined information-flow control monitor (extended version)

We present a novel progress-sensitive, flow-sensitive hybrid information-flow control monitor for an imperative interactive language. Progress-sensitive information-flow control is a strong information security guarantee which ensures that a program's progress (or lack of) does not leak information. Flow-sensitivity means that this strong security guarantee is enforced fairly precisely: our monitor tracks information flow per variable and per program point. We illustrate our approach on an imperative interactive language. Our hybrid monitor is inlined: source programs are translated, by a type-based analysis, into a target language that supports dynamic security levels. A key benefit of this is that the resulting monitored program is amenable to standard optimization techniques such as partial evaluation. One of the distinguishing features of our hybrid monitor is that it uses sets of levels to track the different possible security types of variables. This feature allows us to distinguish outputs that never leak information from those that may leak information.Engineering and Applied Science

Distances for Weighted Transition Systems: Games and Properties

We develop a general framework for reasoning about distances between transition systems with quantitative information. Taking as starting point an arbitrary distance on system traces, we show how this leads to natural definitions of a linear and a branching distance on states of such a transition system. We show that our framework generalizes and unifies a large variety of previously considered system distances, and we develop some general properties of our distances. We also show that if the trace distance admits a recursive characterization, then the corresponding branching distance can be obtained as a least fixed point to a similar recursive characterization. The central tool in our work is a theory of infinite path-building games with quantitative objectives.Comment: In Proceedings QAPL 2011, arXiv:1107.074