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We tackle the problem of non robustness of simulation and bisimulation when dealing with probabilistic processes. It is important to ignore tiny deviations in probabilities because these often come from experience or estimations. A few approaches have been proposed to treat this issue, for example metrics to quantify the non bisimilarity (or closeness) of… (More)

- Mathieu Tracol, Josée Desharnais, Abir Zhioua
- QAPL
- 2011

We present relaxed notions of simulation and bisimulation on Probabilistic Automata (PA), that allow some error ε . When ε = 0 we retrieve the usual notions of bisimulation and simulation on PAs. We give logical characterisations of these notions by choosing suitable logics which differ from the elementary ones, L and L ¬, by the modal operator. Using flow… (More)

- Mathieu Tracol, Christel Baier, Marcus Größer
- FSTTCS
- 2009

In a context of ω-regular specifications for infinite execution sequences, the classical Büchi condition, or repeated liveness condition, asks that an accepting state is visited infinitely often. In this paper, we show that in a probabilistic context it is relevant to strengthen this infinitely often condition. An execution path is now accepting if the… (More)

Low cost mapping using UAV technology is becoming a trendy topic. Many systems exist where a simple camera can be deployed to take images, generally georeferenced with a GPS chip and MEMS attitude sensors. The step from using those images as information picture to photogrammetric products with geo-reference, such as digital terrain model (DTM) or… (More)

- Krishnendu Chatterjee, Martin Chmelik, Mathieu Tracol
- J. Comput. Syst. Sci.
- 2016

We consider partially observable Markov decision processes (POMDPs) with ω-regular conditions specified as parity objectives. The class of ω-regular languages extends regular languages to infinite strings and provides a robust specification language to express all properties used in verification, and parity objectives are canonical forms to express… (More)

- Mathieu Tracol
- Oper. Res. Lett.
- 2009

- Krishnendu Chatterjee, Mathieu Tracol
- 2012 27th Annual IEEE Symposium on Logic in…
- 2012

We consider probabilistic automata on infinite words with acceptance defined by parity conditions. We consider three qualitative decision problems: (i) the positive decision problem asks whether there is a word that is accepted with positive probability; (ii) the almost decision problem asks whether there is a word that is accepted with probability 1; and… (More)

We consider partially observable Markov decision processes (POMDPs) with ω-regular conditions specified as parity objectives. The class of ω-regular languages extends regular languages to infinite strings and provides a robust specification language to express all properties used in verification, and parity objectives are canonical forms to express… (More)

- Michel de Rougemont, Mathieu Tracol
- 2009 24th Annual IEEE Symposium on Logic In…
- 2009

We associate a statistical vector to a trace and a geometrical embedding to a Markov Decision Process, based on a distance on words, and study basic Membership and Equivalence problems. The Membership problem for a trace \textit{w} and a Markov Decision Process \textit{S} decides if there exists a strategy on \textit{S} which generates with high probability… (More)

- Michel de Rougemont, Mathieu Tracol
- CAI
- 2013

We consider networks of Markov Decision Processes (MDPs) where each MDP is one of the N nodes of a graph G. The transition probabilities of an MDP depend on the states of its direct neighbors in the graph, and runs operate by selecting a random node and following a random transition in the chosen device MDP. As the state space of all the configurations of… (More)