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

Modeling and Analysis of Power-Aware Systems

The paper describes a formal approach for designing and reasoning about power-constrained, timed systems. The framework is based on process algebra, a formalism that has been developed to describe and analyze communicating concurrent systems. The proposed extension allows the modeling of probabilistic resource failures, priorities of resource usages, and power consumption by resources within the same formalism. Thus, it is possible to model alternative power-consumption behaviors and analyze tradeoffs in their timing and other characteristics. This paper describes the modeling and analysis techniques, and illustrates them with examples, including a dynamic voltage-scaling algorithm

An Algorithm for Probabilistic Alternating Simulation

In probabilistic game structures, probabilistic alternating simulation (PA-simulation) relations preserve formulas defined in probabilistic alternating-time temporal logic with respect to the behaviour of a subset of players. We propose a partition based algorithm for computing the largest PA-simulation, which is to our knowledge the first such algorithm that works in polynomial time, by extending the generalised coarsest partition problem (GCPP) in a game-based setting with mixed strategies. The algorithm has higher complexities than those in the literature for non-probabilistic simulation and probabilistic simulation without mixed actions, but slightly improves the existing result for computing probabilistic simulation with respect to mixed actions.Comment: We've fixed a problem in the SOFSEM'12 conference versio

Using schedulers to test probabilistic distributed systems

This is the author's accepted manuscript. The final publication is available at Springer via http://dx.doi.org/10.1007/s00165-012-0244-5. Copyright © 2012, British Computer Society.Formal methods are one of the most important approaches to increasing the confidence in the correctness of software systems. A formal specification can be used as an oracle in testing since one can determine whether an observed behaviour is allowed by the specification. This is an important feature of formal testing: behaviours of the system observed in testing are compared with the specification and ideally this comparison is automated. In this paper we study a formal testing framework to deal with systems that interact with their environment at physically distributed interfaces, called ports, and where choices between different possibilities are probabilistically quantified. Building on previous work, we introduce two families of schedulers to resolve nondeterministic choices among different actions of the system. The first type of schedulers, which we call global schedulers, resolves nondeterministic choices by representing the environment as a single global scheduler. The second type, which we call localised schedulers, models the environment as a set of schedulers with there being one scheduler for each port. We formally define the application of schedulers to systems and provide and study different implementation relations in this setting

Timed Parity Games: Complexity and Robustness

We consider two-player games played in real time on game structures with clocks where the objectives of players are described using parity conditions. The games are \emph{concurrent} in that at each turn, both players independently propose a time delay and an action, and the action with the shorter delay is chosen. To prevent a player from winning by blocking time, we restrict each player to play strategies that ensure that the player cannot be responsible for causing a zeno run. First, we present an efficient reduction of these games to \emph{turn-based} (i.e., not concurrent) \emph{finite-state} (i.e., untimed) parity games. Our reduction improves the best known complexity for solving timed parity games. Moreover, the rich class of algorithms for classical parity games can now be applied to timed parity games. The states of the resulting game are based on clock regions of the original game, and the state space of the finite game is linear in the size of the region graph. Second, we consider two restricted classes of strategies for the player that represents the controller in a real-time synthesis problem, namely, \emph{limit-robust} and \emph{bounded-robust} winning strategies. Using a limit-robust winning strategy, the controller cannot choose an exact real-valued time delay but must allow for some nonzero jitter in each of its actions. If there is a given lower bound on the jitter, then the strategy is bounded-robust winning. We show that exact strategies are more powerful than limit-robust strategies, which are more powerful than bounded-robust winning strategies for any bound. For both kinds of robust strategies, we present efficient reductions to standard timed automaton games. These reductions provide algorithms for the synthesis of robust real-time controllers

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

Testing Reactive Probabilistic Processes

We define a testing equivalence in the spirit of De Nicola and Hennessy for reactive probabilistic processes, i.e. for processes where the internal nondeterminism is due to random behaviour. We characterize the testing equivalence in terms of ready-traces. From the characterization it follows that the equivalence is insensitive to the exact moment in time in which an internal probabilistic choice occurs, which is inherent from the original testing equivalence of De Nicola and Hennessy. We also show decidability of the testing equivalence for finite systems for which the complete model may not be known

Assume-Guarantee Abstraction Refinement for Probabilistic Systems

We describe an automated technique for assume-guarantee style checking of strong simulation between a system and a specification, both expressed as non-deterministic Labeled Probabilistic Transition Systems (LPTSes). We first characterize counterexamples to strong simulation as "stochastic" trees and show that simpler structures are insufficient. Then, we use these trees in an abstraction refinement algorithm that computes the assumptions for assume-guarantee reasoning as conservative LPTS abstractions of some of the system components. The abstractions are automatically refined based on tree counterexamples obtained from failed simulation checks with the remaining components. We have implemented the algorithms for counterexample generation and assume-guarantee abstraction refinement and report encouraging results.Comment: 23 pages, conference paper with full proof

Ambient Air Pollution, Social Inequalities and Asthma Exacerbation in Greater Strasbourg (France) Metropolitan Area: the PAISA Study

International audienceThe socio-economic status (SES) of populations has an influence on the incidence or mortality rates of numerous health outcomes, among which respiratory diseases (Prescott et al., 2003; Ellison-Loschmann et al., 2007). Considering asthma, the possible contribution of SES to overall prevalence –regardless of asthma severity-, remains controversial in industrialized countries. Several studies indicate that allergic asthma is more prevalent in more well-off populations whereas the non-allergic forms of asthma are more common in the deprived ones (Cesaroni et al., 2003; Blanc et al., 2006). On the other hand, severe asthma whatever its etiology appears to be more frequent in the latter populations, as compared to the more affluent (Basagana et al., 2004). Risk factors for exacerbations (e.g., passive smoking (Wright Subramanian, 2007), psychosocial stress (Gold & Wright, 2005), cockroach allergens (Kitch et al., 2000), and suboptimal compliance with anti-inflammatory medication (Gottlieb et al., 1995)) are generally more common among people with asthma and low SES than their better-off counterparts. These observations support the hypothesis that some factors more present in deprived populations contribute to asthma exacerbation (Mielck et al., 1996)

Probabilistic Bisimulation: Naturally on Distributions

In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for probabilistic systems corresponding to this view that treats probability distributions as first-class citizens. Our definition applies in the same way to discrete systems as well as to systems with uncountable state and action spaces. Several examples demonstrate that our definition refines the understanding of behavioural equivalences of probabilistic systems. In particular, it solves a long-standing open problem concerning the representation of memoryless continuous time by memory-full continuous time. Finally, we give algorithms for computing this bisimulation not only for finite but also for classes of uncountably infinite systems