Synthesis for PCTL in Parametric Markov Decision Processes

Hahn, Ernst Moritz; Han, Tingting; Zhang, Lijun

doi:10.1007/978-3-642-20398-5_12

Cited by 70 publications

(76 citation statements)

References 18 publications

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“…This algorithm builds upon our previous work concerning solving the problem of PCTL model checking for PMDPs [6].…”

Section: A Region-based Methodsmentioning

confidence: 99%

“…In [6], we assumed that for all parameters we are given a certain range, that is, a lower and upper bound for the values of this parameter. Consequently, all parameter valuations respecting these bounds are valid, with finitely many exceptions, and the area of valid evaluations (parameter space) forms a hyper-rectangle.…”

Section: A Region-based Methodsmentioning

confidence: 99%

“…In the resulting PMDP, these transitions thus have the probabilities p 1 = 0.3 + x 1 , p 2 = 0.3 + x 2 , and p 3 = 0.4 − x 1 − x 2 . Because of this, to ensure that all probabilities are nonnegative, the area of valid evaluations is now a triangle, as depicted in Figure 1 a), and the parameter space is no longer a hyper-rectangle as assumed in [6].…”

Section: A Region-based Methodsmentioning

confidence: 99%

“…The first variant is a region-based approach, which builds on our work on parametric MDPs [6] (see also [7] for a related approach). A region represents a set of parameter valuations.…”

Section: Introductionmentioning

confidence: 99%

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Model Repair for Markov Decision Processes

Chen

Hahn

Han

et al. 2013

2013 International Symposium on Theoretical Aspects of Software Engineering

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Abstract-Markov decision processes (MDPs) are often used for modelling distributed systems with probabilistic failure or randomisation. We consider the problem of model repair for MDPs defined as follows: if the MDP fails to satisfy a property, we aim to find new values for the transition probabilities so that the property is guaranteed to hold, while at the same time the cost of repair is minimised. Because solving the MDP repair problem exactly is infeasible, in this paper we focus on approximate solution methods. We first formulate a region-based approach, which yields an interval in which the minimal repair cost is contained. As an alternative, we also consider samplingbased approaches, which are faster but unable to provide lower bounds on the repair cost. We have integrated both methods into the probabilistic model checker PRISM and demonstrated their usefulness in practice using a computer virus case study.

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“…This algorithm builds upon our previous work concerning solving the problem of PCTL model checking for PMDPs [6].…”

Section: A Region-based Methodsmentioning

confidence: 99%

Section: A Region-based Methodsmentioning

confidence: 99%

Section: A Region-based Methodsmentioning

confidence: 99%

“…The first variant is a region-based approach, which builds on our work on parametric MDPs [6] (see also [7] for a related approach). A region represents a set of parameter valuations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Model Repair for Markov Decision Processes

Chen

Hahn

Han

et al. 2013

2013 International Symposium on Theoretical Aspects of Software Engineering

Self Cite

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“…To improve efficiency, one can employ parametric approaches, e.g. [21], and specifically parameter synthesis [28]. We consider parametric probabilistic models, where probabilities are specified in terms of expressions over parameters, rather than concrete values.…”

Section: Adaptivenessmentioning

confidence: 99%

Advances in Quantitative Verification for Ubiquitous Computing

Kwiatkowska

2013

Theoretical Aspects of Computing – ICTAC 2013

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Abstract. Ubiquitous computing, where computers 'disappear' and instead sensor-enabled and software-controlled devices assist us in everyday tasks, has become an established trend. To ensure the safety and reliability of software embedded in these devices, rigorous model-based design methodologies are called for. Quantitative verification, a powerful technique for analysing system models against quantitative properties such as "the probability of a data packet being delivered within 1ms to a nearby Bluetooth device is at least 0.98", has proved useful by detecting and correcting flaws in a number of ubiquitous computing applications. In this paper, we focus on three key aspects of ubiquitous computing: autonomous behaviour, constrained resources and adaptiveness. We summarise recent advances of quantitative verification in relation to these aspects, illustrating each with a case study analysed using the probabilistic model checker PRISM. The paper concludes with an outline of future challenges that remain in this area.

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Accelerated Model Checking of Parametric Markov Chains

Gainer

Hahn

Schewe

2018

Automated Technology for Verification and Analysis

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Parametric Markov chains occur quite naturally in various applications: they can be used for a conservative analysis of probabilistic systems (no matter how the parameter is chosen, the system works to specification); they can be used to find optimal settings for a parameter; they can be used to visualise the influence of system parameters; and they can be used to make it easy to adjust the analysis for the case that parameters change. Unfortunately, these advancements come at a cost: parametric model checking is-or rather was-often slow. To make the analysis of parametric Markov models scale, we need three ingredients: clever algorithms, the right data structure, and good engineering. Clever algorithms are often the main (or sole) selling point; and we face the trouble that this paper focuses on -the latter ingredients to efficient model checking. Consequently, our easiest claim to fame is in the speedup we have often realised when comparing to the state of the art.

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Synthesis for PCTL in Parametric Markov Decision Processes

Cited by 70 publications

References 18 publications

Model Repair for Markov Decision Processes

Model Repair for Markov Decision Processes

Advances in Quantitative Verification for Ubiquitous Computing

Accelerated Model Checking of Parametric Markov Chains

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