Model Checking HPnGs in Multiple Dimensions: Representing State Sets as Convex Polytopes

Hüls, Jannik; Remke, Anne

doi:10.1007/978-3-030-21759-4_9

Cited by 9 publications

(12 citation statements)

References 31 publications

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“…While the NUM intervals method performs best in this setting, it can only be used to compute transient distributions. Model checking, as proposed in [33] requires geometric operations and hence, integration on polytopes.…”

Section: Computation and Validation Of Resultsmentioning

confidence: 99%

See 1 more Smart Citation

State-Space Construction of Hybrid Petri Nets with Multiple Stochastic Firings

Hüls

Pilch

Schinke

et al. 2019

Quantitative Evaluation of Systems

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Hybrid Petri nets have been extended to include general transitions that fire after a randomly distributed amount of time. With a single general one-shot transition the state space and evolution over time can be represented either as a Parametric Location Tree or as a Stochastic Time Diagram. Recent work has shown that both representations can be combined and then allow multiple stochastic firings. This work presents an algorithm for building the Parametric Location Tree with multiple general transition firings and shows how its transient probability distribution can be computed using multi-dimensional integration. We discuss the (dis-)advantages of an interval arithmetic and a geometric approach to compute the areas of integration. Furthermore, we provide details on how to perform a Monte Carlo integration either directly on these intervals or convex polytopes, or after transformation to standard simplices. A case study on a battery-backup system shows the feasibility of the approach and discusses the performance of the different integration approaches.

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Section: Computation and Validation Of Resultsmentioning

confidence: 99%

“…for a predefined maximum time. As such, this paper provides the missing link to recent work [33,34] which provides model checking capabilities for HPnGs with multiple random variables, assuming the existence of the PLT.…”

mentioning

confidence: 99%

State-Space Construction of Hybrid Petri Nets with Multiple Stochastic Firings

Hüls

Pilch

Schinke

et al. 2019

Quantitative Evaluation of Systems

Self Cite

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show abstract

“…This article shows how the state-space of a Hybrid Petri net with multiple general transition firings can be constructed as a Parametric Location Tree (PLT) [24] for a predefined maximum time. As such, this article provides the missing link to recent work [33,34] that provides model checking capabilities for HPnGs with multiple random variables, assuming the existence of the PLT.…”

Section: Introductionmentioning

confidence: 99%

“…However, it is possible to compute a geometric representation for each location in a PLT [34] that fully relies on halfspace intersection, which can be solved e.g., using quickhull [4] also for higher dimensions. This combines the computational speed of the parametric reachability analysis with the ease that a geometric representation brings for model checking complex properties [33].…”

Section: Introductionmentioning

confidence: 99%

State-space Construction of Hybrid Petri Nets with Multiple Stochastic Firings

Hüls

Pilch

Schinke

et al. 2021

ACM Trans. Model. Comput. Simul.

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Hybrid Petri nets have been extended to include general transitions that fire after a randomly distributed amount of time. With a single general one-shot transition the state space and evolution over time can be represented either as a Parametric Location Tree or as a Stochastic Time Diagram . Recent work has shown that both representations can be combined and then allow multiple stochastic firings. This work presents an algorithm for building the Parametric Location Tree with multiple general transition firings and shows how its transient probability distribution can be computed using multi-dimensional integration. We discuss the (dis-)advantages of an interval arithmetic and a geometric approach to compute the areas of integration. Furthermore, we provide details on how to perform a Monte Carlo integration either directly on these intervals or convex polytopes, or after transformation to standard simplices. A case study on a battery-backup system shows the feasibility of the approach and discusses the performance of the different integration approaches.

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“…hpnmg The tool hpnmg [36] is a model checker for Hybrid Petri nets with an arbitrary but finite number of general transition firings against specifications formulated in STL [38]. Each general transition firing results in a random variable which follows a continuous probability distribution.…”

Section: Participating Tools and Frameworkmentioning

confidence: 99%

ARCH-COMP20 Category Report: Stochastic Models

Abate¹,

Blom²,

Cauchi³

et al.

EPiC Series in Computing

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This report presents the results of a friendly competition for formal verification and policy synthesis of stochastic models. It also introduces new benchmarks within this category, and recommends next steps for this category towards next year’s edition of the competition. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in Spring/Summer 2020.

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Model Checking HPnGs in Multiple Dimensions: Representing State Sets as Convex Polytopes

Cited by 9 publications

References 31 publications

State-Space Construction of Hybrid Petri Nets with Multiple Stochastic Firings

State-Space Construction of Hybrid Petri Nets with Multiple Stochastic Firings

State-space Construction of Hybrid Petri Nets with Multiple Stochastic Firings

ARCH-COMP20 Category Report: Stochastic Models

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