Probabilistic regular graphs

Deterministic graph grammars generate regular graphs, that form a structural extension of configuration graphs of pushdown systems. In this paper, we study a probabilistic extension of regular graphs obtained by labelling the terminal arcs of the graph grammars by probabilities. Stochastic properties of these graphs are expressed using PCTL, a probabilistic extension of computation tree logic. We present here an algorithm to perform approximate verification of PCTL formulae. Moreover, we prove that the exact model-checking problem for PCTL on probabilistic regular graphs is undecidable, unless restricting to qualitative properties. Our results generalise those of EKM06, on probabilistic pushdown automata, using similar methods combined with graph grammars techniques.Comment: In Proceedings INFINITY 2010, arXiv:1010.611

Verifying nondeterministic probabilistic channel systems against ω\omega-regular linear-time properties

Lossy channel systems (LCSs) are systems of finite state automata that communicate via unreliable unbounded fifo channels. In order to circumvent the undecidability of model checking for nondeterministic LCSs, probabilistic models have been introduced, where it can be decided whether a linear-time property holds almost surely. However, such fully probabilistic systems are not a faithful model of nondeterministic protocols. We study a hybrid model for LCSs where losses of messages are seen as faults occurring with some given probability, and where the internal behavior of the system remains nondeterministic. Thus the semantics is in terms of infinite-state Markov decision processes. The purpose of this article is to discuss the decidability of linear-time properties formalized by formulas of linear temporal logic (LTL). Our focus is on the qualitative setting where one asks, e.g., whether a LTL-formula holds almost surely or with zero probability (in case the formula describes the bad behaviors). Surprisingly, it turns out that -- in contrast to finite-state Markov decision processes -- the satisfaction relation for LTL formulas depends on the chosen type of schedulers that resolve the nondeterminism. While all variants of the qualitative LTL model checking problem for the full class of history-dependent schedulers are undecidable, the same questions for finite-memory scheduler can be solved algorithmically. However, the restriction to reachability properties and special kinds of recurrent reachability properties yields decidable verification problems for the full class of schedulers, which -- for this restricted class of properties -- are as powerful as finite-memory schedulers, or even a subclass of them.Comment: 39 page

Determinacy and Decidability of Reachability Games with Partial Observation on Both Sides

We prove two determinacy and decidability results about two-players stochastic reachability games with partial observation on both sides and finitely many states, signals and actions

Bounded Satisfiability for PCTL

While model checking PCTL for Markov chains is decidable in polynomial-time, the decidability of PCTL satisfiability, as well as its finite model property, are long standing open problems. While general satisfiability is an intriguing challenge from a purely theoretical point of view, we argue that general solutions would not be of interest to practitioners: such solutions could be too big to be implementable or even infinite. Inspired by bounded synthesis techniques, we turn to the more applied problem of seeking models of a bounded size: we restrict our search to implementable -- and therefore reasonably simple -- models. We propose a procedure to decide whether or not a given PCTL formula has an implementable model by reducing it to an SMT problem. We have implemented our techniques and found that they can be applied to the practical problem of sanity checking -- a procedure that allows a system designer to check whether their formula has an unexpectedly small model

Entre substance et figurativité. Le discours critique de la poésie

Fondé sur trois ouvrages récents consacrés à la poésie contemporaine, l'article fait apparaître une problématique propre à ce discours critique : la présence et le statut d'une dimension figurative en son sein. Au delà d'une simple stratégie persuasive de séduction dont le post-formalisme renouvelle la possibilité, cette pratique du figuratif renvoie à la question de la substance en relation avec la forme. On explicite alors le lien paradoxal qui unit le discours critique à son objet, la poésie contemporaine incorporant dans son exercice une interrogation métalinguistique, et le métalangage critique incorporant quant à lui une dimension figurative du discours pour signifier une proximité sensible avec l'expérience poétique, inaccessible au seul langage conceptuel. Ces parcours inversés inscrivent, dans le discours critique, une poéticité de second degré.Based upon three recently published works, devoted to contemporary French poetry, the article focuses the problem of a figurative dimension as a part of this criticism genre. Far from being a seduction persuasive technique, the possibility of which the actual post-formalism era could have renewed, this presence of figurativity inside a cognitive discourse refers to the specific relationship between "substance" and "form" in poetic expression. A paradoxal tie then appears, tightly connecting critical discourse with its object : as contemporary poetry incorporates a metalinguistic interrogation into its language, criticist metalanguage incorporates a figurative dimension in order to express and explain a sensitive closeness with poetic experience, that an abstract descriptive language could not signify. Those two reversal ways set up a second degree poeticity in criticism writing

When are Stochastic Transition Systems Tameable?

A decade ago, Abdulla, Ben Henda and Mayr introduced the elegant concept of decisiveness for denumerable Markov chains [1]. Roughly speaking, decisiveness allows one to lift most good properties from finite Markov chains to denumerable ones, and therefore to adapt existing verification algorithms to infinite-state models. Decisive Markov chains however do not encompass stochastic real-time systems, and general stochastic transition systems (STSs for short) are needed. In this article, we provide a framework to perform both the qualitative and the quantitative analysis of STSs. First, we define various notions of decisiveness (inherited from [1]), notions of fairness and of attractors for STSs, and make explicit the relationships between them. Then, we define a notion of abstraction, together with natural concepts of soundness and completeness, and we give general transfer properties, which will be central to several verification algorithms on STSs. We further design a generic construction which will be useful for the analysis of {\omega}-regular properties, when a finite attractor exists, either in the system (if it is denumerable), or in a sound denumerable abstraction of the system. We next provide algorithms for qualitative model-checking, and generic approximation procedures for quantitative model-checking. Finally, we instantiate our framework with stochastic timed automata (STA), generalized semi-Markov processes (GSMPs) and stochastic time Petri nets (STPNs), three models combining dense-time and probabilities. This allows us to derive decidability and approximability results for the verification of these models. Some of these results were known from the literature, but our generic approach permits to view them in a unified framework, and to obtain them with less effort. We also derive interesting new approximability results for STA, GSMPs and STPNs.Comment: 77 page

Numerical Model for Oxide Scale Growth with Explicit Treatment of Vacancy Fluxes

In the framework of research on behaviour of nuclear waste containers, to evaluate the effects of possible evolution of experimental conditions, as well as evolution of parameters controlling oxidation rate during long-term interim storage, a numerical model has been developed in order to take into account non-stationary states. To anticipate effects like cold working of the metal on the scale growth kinetics and risks of scale detachment by over saturation of vacancies at the metal/oxide interface in the course of scale growth, the model is based on the calculation of chemical species, but also vacancies profiles evolution in the oxide and the metal following a simple time integration. An original numerical treatment is proposed to easily describe elimination of vacancies by introducing sink strength in the metal. The first calculations are presented and discussed

Low Temperature Oxidation of pure Iron : Growth kinetics and scale Morphologies

Isothermal oxidation of pure iron has been performed in air at atmospheric pressure between 260°C and 500°C. Growth kinetics are accurately analysed and scale morphologies are investigated by SEM and TEM observations. The calculation of the variations of the parabolic rate constant kp with scale thickness allows a better understanding of scale growth mechanisms involved at this intermediate temperature range, which have been poorly investigated up to now. These results are discussed with the objective of long term behaviour for long term interim storage of some nuclear waste containers