Parametric Interval Markov Chains (pIMCs) are a specification formalism that extend Markov Chains (MCs) and Interval Markov Chains (IMCs) by taking into account imprecision in the transition probability values: transitions in pIMCs are labeled with parametric intervals of probabilities. In this work, we study the difference between pIMCs and other Markov Chain abstractions models and investigate the two usual semantics for IMCs: once-and-for-all and at-every-step. In particular, we prove that both semantics agree on the maximal/minimal reachability probabilities of a given IMC. We then investigate solutions to several parameter synthesis problems in the context of pIMCs -consistency, qualitative reachability and quantitative reachability -that rely on constraint encodings. Finally, we propose a prototype implementation of our constraint encodings with promising results.

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Unmanned Aerial Vehicles (UAV) are now widespread in our society and are often used in a context where they can put people at risk. Studying their reliability, in particular in the context of flight above a crowd, thus becomes a necessity. In this paper, we study the modeling and analysis of UAV in the context of their flight plan. To this purpose, we build a parametric probabilistic model of the UAV and use it, as well as a given flight plan, in order to model its trajectory. This model takes into account parameters such as potential filter or sensor (like GPS) failure as well as wind force and direction. Because of the nature and complexity of the successive obtained models, their exact verification using tools such as PRISM or PARAM is impossible. We therefore develop a new approximation method, called Parametric Statistical Model Checking, in order to compute failure probabilities. This method has been implemented in a prototype tool, which we use to resolve complex issues in a practical case study.

0000−0001−8473−9555] , Benoit Delahaye 4[0000−0002−9104−4361] , Paulin Fournier 4 , and Didier Lime 5[0000−0001−9429−7586]Abstract. In this paper we consider state reachability in networks composed of many identical processes running a parametric timed broadcast protocol (PTBP). PTBP are a new model extending both broadcast protocols and parametric timed automata. This work is, up to our knowledge, the first to consider the combination of both a parametric network size and timing parameters in clock guard constraints. Since the communication topology is of utmost importance in broadcast protocols, we investigate reachability problems in both clique semantics where every message reaches every processes, and in reconfigurable semantics where the set of receivers is chosen non-deterministically. In addition, we investigate the decidability status depending on whether the timing parameters in guards appear only as upper bounds in guards (U-PTBP), as lower bounds (L-PTBP) or when the set of parameters is partitioned in lower-bound and upper-bound parameters (L/U-PTBP).The application of model-checking to real-life complex systems faces several problems, and for many of them the use of parameters, i. e., symbolic constants representing an unknown quantity can be part of the solution. First, for big systems, the so-called state-space explosion limits the practical applicability of ⋆ This is the author (and extended) version of the manuscript of the same name published in the proceedings of the 20th International Conference on Verification, Model Checking, and Abstract Interpretation (VMCAI 2019). The final version is available at http://dx.

We show that one can decide if a rational equivalence relation can be given as the equivalence kernel of a sequential letter-to-letter transduction. This problem comes from the setting of games with imperfect information. In [1, p. 6] the authors propose to model imperfect information by a rational equivalence relation and leave open the problem of deciding if one can synthesize a sequential letter-to-letter transducer (Mealy machine) which maps equivalent histories to the same sequence of observations. We also show that knowing if an equivalence relation can be given as the equivalence kernel of a sequential transducer is undecidable, even if the relation is given as a letter-to-letter transducer.