Model Checking Durational Probabilistic Systems

Laroussinie, François; Sproston, Jeremy

doi:10.1007/978-3-540-31982-5_9

Cited by 20 publications

(25 citation statements)

References 20 publications

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“…The basic idea of [27,34] is to implicitly unfold the MDP along cost epochs, and exploit the regularities of the epoch-MDPs. Prism [37] and the Modest Toolset [29] have been updated with such methods for the single-objective case and significantly outperform the explicit unfolding approach of [2,40]. This paper presents an algorithm that lifts this principle to multiple cost objectives and determines approximation errors when using value iteration.…”

Section: Introductionmentioning

confidence: 99%

Multi-cost Bounded Reachability in MDP

Hartmanns

Junges

Katoen

et al. 2018

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. We provide an efficient algorithm for multi-objective modelchecking problems on Markov decision processes (MDPs) with multiple cost structures. The key problem at hand is to check whether there exists a scheduler for a given MDP such that all objectives over cost vectors are fulfilled. Reachability and expected cost objectives are covered and can be mixed. Empirical evaluation shows the algorithm's scalability. We discuss the need for output beyond Pareto curves and exploit the available information from the algorithm to support decision makers.

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Section: Introductionmentioning

confidence: 99%

Multi-cost Bounded Reachability in MDP

Hartmanns

Junges

Katoen

et al. 2018

Tools and Algorithms for the Construction and Analysis of Systems

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“…An EXPTIME algorithm can be obtained by employing the algorithms of [LS05]. We now prove EXPTIME-hardness of Ptctl 0/1 model checking on discrete TMDPs by a reduction from countdown games.…”

Section: Model Checkingmentioning

confidence: 94%

Model Checking Probabilistic Timed Automata with One or Two Clocks

Jurdziński¹,

Laroussinie²,

Sproston³

2008

Logical Methods in Computer Science

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Abstract. Probabilistic timed automata are an extension of timed automata with discrete probability distributions. We consider model-checking algorithms for the subclasses of probabilistic timed automata which have one or two clocks. Firstly, we show that Pctl probabilistic model-checking problems (such as determining whether a set of target states can be reached with probability at least 0.99 regardless of how nondeterminism is resolved) are PTIME-complete for one-clock probabilistic timed automata, and are EXPTIME-complete for probabilistic timed automata with two clocks. Secondly, we show that, for one-clock probabilistic timed automata, the model-checking problem for the probabilistic timed temporal logic Ptctl is EXPTIME-complete. However, the model-checking problem for the subclass of Ptctl which does not permit both punctual timing bounds, which require the occurrence of an event at an exact time point, and comparisons with probability bounds other than 0 or 1, is PTIME-complete for one-clock probabilistic timed automata.

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“…We also consider the class of structurally non-Zeno well-formed PDPTAs and parameter valuations (originally adapted from [32] and considered for probabilistic systems in [27]), in which all loops of the graph of the PDPTA obtained from the set of locations L and set of edges E A involve the passage of at least 1 time unit. …”

Section: Definition 3 a Pdpta A With A Parameter Valuation κ Is Well mentioning

confidence: 99%

Computing Expected Absorption Times for Parametric Determinate Probabilistic Timed Automata

Chamseddine

Duflot

Fribourg

et al. 2008

2008 Fifth International Conference on Quantitative Evaluation of Systems

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We consider a variant of probabilistic timed automata called parametric determinate probabilistic timed automata. Such automata are fully probabilistic: there is a single distribution of outgoing transitions from each of the automaton's nodes, and it is possible to remain at a node only for a given amount of time. The residence time within a node may be given in terms of a parameter, and hence we do not assume that its concrete value is known. We claim that, often in practice, the maximal expected time to reach a given absorbing node of a probabilistic timed automaton can be captured using a parametric determinate probabilistic timed automaton. We give a method for computing the expected time for a parametric determinate probabilistic timed automaton to reach an absorbing node. The method consists in constructing a variant of a Markov chain with costs (where the costs correspond to durations), and is parametric in the sense that the expected absorption time is computed as a function of the model's parameters. The complexity of the analysis is independent from the maximal constant bounding the values of the clocks, and is polynomial in the number of edges of the original parametric determinate probabilistic timed automaton.

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Model Checking Durational Probabilistic Systems

Cited by 20 publications

References 20 publications

Multi-cost Bounded Reachability in MDP

Multi-cost Bounded Reachability in MDP

Model Checking Probabilistic Timed Automata with One or Two Clocks

Computing Expected Absorption Times for Parametric Determinate Probabilistic Timed Automata

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