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A finite state Markov chain M is often viewed as a probabilistic transition system. An alternative view - which we follow here - is to regard M as a linear transform operating on the space of probability distributions over its set of nodes. The novel idea here is to discretize the probability value space [0,1] into a finite set of intervals. A concrete(More)
We consider the following decision problem: given a finite Markov chain with distinguished source and target states, and given a rational number r, does there exist an integer n such that the probability to reach the target from the source in n steps is r? This problem, which is not known to be decidable, lies at the heart of many model checking questions(More)
We consider message sequence charts enriched with timing constraints between pairs of events. As in the untimed setting, an infinite family of time-constrained message sequence charts (TC-MSCs) is generated using an HMSC—a finite-state automaton whose nodes are labelled by TC-MSCs. A timed MSC is an MSC in which each event is assigned an explicit(More)
We consider the problem of model checking message-passing systems with real-time requirements. As behavioural specifications, we use message sequence charts (MSCs) annotated with timing constraints. Our system model is a network of communicating finite state machines with local clocks, whose global behaviour can be regarded as a timed automaton. Our goal is(More)
We provide a framework for distributed systems that impose timing constraints on their executions. We propose a timed model of communicating finite-state machines, which communicate by exchanging messages through channels and use event clocks to generate collections of timed message sequence charts (T-MSCs). As a specification language, we propose a monadic(More)
Rapport de recherche n° 7823 — November 2011 — 15 pages Résumé : Il est notoirement difficile d'analyser les comportements de systémes décrits par des modèles qui comportentà la fois du temps et de la concurrence. Des résultats de décidabilité existent pour des modèles dans lesquels les valeurs des horloges sur différents processus ne peuvent pasêtre(More)
Structural and genetic studies on prokaryotic ribosomes have provided important insights into fundamental aspects of protein synthesis and translational control and its interaction with ribosomal drugs. Comparable mechanistic studies in eukaryotes are mainly hampered by the absence of both high-resolution crystal structures and efficient genetic models. To(More)
Verifying systems involving both time and concurrency rapidly leads to undecidability, and requires restrictions to become effective. This paper addresses the emptiness problem for time-constrained MSC-Graphs (TC-MSC graphs for short), that is, checking whether there is a timed execution compatible with a TC-MSC graph specification. This problem is known to(More)