Diagnosis in Infinite-State Probabilistic Systems

In a recent work, we introduced four variants of diagnosability (FA, IA, FF, IF) in (finite) probabilistic systems (pLTS) depending whether one considers (1) finite or infinite runs and (2) faulty or all runs. We studied their relationship and established that the corresponding decision problems are PSPACE-complete. A key ingredient of the decision procedures was a characterisation of diagnosability by the fact that a random run almost surely lies in an open set whose specification only depends on the qualitative behaviour of the pLTS. Here we investigate similar issues for infinite pLTS. We first show that this characterisation still holds for FF-diagnosability but with a G-delta set instead of an open set and also for IF- and IA-diagnosability when pLTS are finitely branching. We also prove that surprisingly FA-diagnosability cannot be characterised in this way even in the finitely branching case. Then we apply our characterisations for a partially observable probabilistic extension of visibly pushdown automata (POpVPA), yielding EXPSPACE procedures for solving diagnosability problems. In addition, we establish some computational lower bounds and show that slight extensions of POpVPA lead to undecidability

Intelligent Modeling and Verification (Editorial)

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Diagnosis and Opacity Problems for Infinite State Systems Modeled by Recursive Tile Systems

International audienceThe analysis of discrete event systems under partial observation is an important topic, with major applications such as the detection of information flow and the diagnosis of faulty behaviors. These questions have, mostly, not been addressed for classical models of recursive systems, such as pushdown systems and recursive state machines. In this paper, we consider recursive tile systems, which are recursive infinite systems generated by a finite collection of finite tiles, a simplified variant of deterministic graph grammars (slightly more general than pushdown systems). Since these systems are infinite-state in general powerset constructions for monitoring do not always apply. We exhibit computable conditions on recursive tile systems and present non-trivial constructions that yield effective computation of the monitors.We apply these results to the classic problems of state-based opacity and diagnosability (off-line verification of opacity and diagnosability, and also run-time monitoring of these properties). For a decidable subclass of recursive tile systems, we also establish the decidability of the problems of state-based opacity and diagnosability

Intelligent Modeling and Verification

System modeling tends to have many complex features, and uncertainties often lead to numerous complications and influence many important aspects related to its applications. Intelligent modeling merges mathematical and computer based approaches, and it utilizes pioneering new scientific methods and cutting-edge technologies

Diagnostic, opacité et test de conformité pour des systèmes récursifs

L'une des façons les plus efficace de s'assurer du bon fonctionnement d'un système informatique est de les représenter par des modèles mathématiques. De nombreux travaux ont été réalisés en utilisant des automates finis comme modèles, nous essayons ici d'étendre ces travaux à des modèles infinis. Dans cette thèse, nous nous intéressons à quelques problèmes dans lesquels un système est observé de façon incomplète. Dans ce cas, il est impossible d'accéder à certaines informations internes. La diagnosticabilité d'une propriété donnée consiste à vérifier qu'à l'exécution du système, un observateur sera en mesure de déterminer avec certitude que la propriété est vérifiée par le système. L'opacité consiste, réciproquement, à déterminer qu'un doute existera toujours. Une autre application concerne la génération de cas de test. Une fois encore, on considère qu'un observateur n'accède qu'à une partie des événements se produisant dans le système (en général les entrées et les sorties). À partir d'une spécification, on produit automatiquement des cas de test, qui ont pour but de détecter des non-conformités (elles même formalisées de façon précise). Ces trois problèmes ont été étudiés pour des modèles finis. Dans cette thèse, nous étendons leur étude aux modèles récursifs, pour cela nous avons introduit notre propre modèle, les RTS, qui sont une généralisation des automates à pile, et d'autres modèles de la récursivité. Nous adaptons ensuite les techniques utilisées sur des modèles finis, qui servent à résoudre les problèmes qui nous intéressent.An effective way to ensure the proper functioning of a computer system is to represent it by using mathematical models . Many studies have been conducted using finite automata as models, in this thesis we try to extend these works to infinite models. We focus on three problems in which a system is partially observed. In this case, it is impossible to access certain internal informations. Diagnosability of a given property consist in checking, that, during the execution of the system, an observer will be able to determine with certainty that the property is verified by the system. Conversely, the opacity consists in determining if a doubt will always exist. Another application is the generation of test cases. Once again, we consider that an observer accesses only some events of the system (typically the inputs and outputs): from a specification, we automatically generate test cases, which are designed to detect non-conformance. These three problems have been studied for finite models. In this thesis, we extend their study to recursive models. For this purpose, we have introduced a new model, the RTS, which are a generalization of pushdown automata and other models of recursion. In order to solve problems of interest, we adapt the techniques used in finite models.RENNES1-Bibl. électronique (352382106) / SudocSudocFranceF

Quantitative Verification of Opacity Properties in Security Systems

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