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

Analysing Decisive Stochastic Processes

In 2007, Abdulla et al. introduced the elegant concept of decisive Markov chain. Intuitively, decisiveness allows one to lift the good properties of finite Markov chains to infinite Markov chains. For instance, the approximate quantitative reachability problem can be solved for decisive Markov chains (enjoying reasonable effectiveness assumptions) including probabilistic lossy channel systems and probabilistic vector addition systems with states. In this paper, we extend the concept of decisiveness to more general stochastic processes. This extension is non trivial as we consider stochastic processes with a potentially continuous set of states and uncountable branching (common features of real-time stochastic processes). This allows us to obtain decidability results for both qualitative and quantitative verification problems on some classes of real-time stochastic processes, including generalized semi-Markov processes and stochastic timed automat

Decisiveness of Stochastic Systems and its Application to Hybrid Models (Full Version)

In [ABM07], Abdulla et al. introduced the concept of decisiveness, an interesting tool for lifting good properties of finite Markov chains to denumerable ones. Later, this concept was extended to more general stochastic transition systems (STSs), allowing the design of various verification algorithms for large classes of (infinite) STSs. We further improve the understanding and utility of decisiveness in two ways. First, we provide a general criterion for proving decisiveness of general STSs. This criterion, which is very natural but whose proof is rather technical, (strictly) generalizes all known criteria from the literature. Second, we focus on stochastic hybrid systems (SHSs), a stochastic extension of hybrid systems. We establish the decisiveness of a large class of SHSs and, under a few classical hypotheses from mathematical logic, we show how to decide reachability problems in this class, even though they are undecidable for general SHSs. This provides a decidable stochastic extension of o-minimal hybrid systems. [ABM07] Parosh A. Abdulla, Noomene Ben Henda, and Richard Mayr. 2007. Decisive Markov Chains. Log. Methods Comput. Sci. 3, 4 (2007).Comment: Full version of GandALF 2020 paper (arXiv:2001.04347v2), updated version of arXiv:2001.04347v1. 30 pages, 6 figure

Tumeur cérébrale multiple avec syndrome de Foster Kennedy :gliomes du corps calleux et du lobe temporal, méningiome du nerf optique

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Stase papillaire après rachianesthésie

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Long-term results of endoscopic sinus surgery in cystic fibrosis

Cystic fibrosis is the most common substantially lethal hereditary disease among young Caucasians (1). That infectious and polypoid degeneration of the nasal mucosa is part of this condition had not been recognized by the otolaryngologist until 1959 (2). The frequency of nasal polyposis in children is extremely low, about 0.1% (3). Schwachmann et al. (1962) (4) found nasal polyposis in 6.7%, Cepero et al. (1987) (5) in 10%, Neely et al. (1972) (6) in 24% and Stern et al. (1982) (7) in 26% of the patients with cystic fibrosis. Settipane (8) stated that any child of 16 years or younger with nasal polyps should be evaluated for cystic fibrosis. He found in cystic fibrosis the prevalence of nasal polyps to be 20%. Later the prevalence was estimated to be 32% in children and 40-48% in adults with cystic fibrosis (9), but at the same time these authors state that the detection of nasal polyps may be limited by the ability of the young child to tolerate nasal examination.SCOPUS: ch.binfo:eu-repo/semantics/publishe

Gliome du nerf optique étendu de la paille au chiasma

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Local gigantism of the hand associated with a plexiform neurofibroma of the ulnar nerve. Report of a case

Report of a case of soft tissue hypertrophy of the ulnar area of the hand and of the fifth finger with hyperpathic anesthesia in the same region. This hypertrophy existed at birth, as well as a large nevus verrucosus of the axilla. Many years later, a plexiform neurofibroma of the ulnar nerve developed at the elbow level. The resection of the neurofibroma, of the hypertrophied finger and partly of the ulnar region of the palm was followed by an excellent functional result. The causal relationship between a lesion of the nervous system and the local gigantism is debated. The embryologic or teratologic theory which implies a disturbance of induction seems most probable.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Volumineux gliome kystique du chiasma à symptomatologie cérébrale prédominante

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