Quantitative variability modelling and analysis

Beek, Maurice H. ter; Legay, Axel

doi:10.1007/s10009-019-00535-1

“…The methods presented in [13,22] exploit a repetitive structure in parametric MCs to accelerate the construction of closed form solutions and are not applicable to MDPs. Parametric models have been used to support the design of systems [2,8] or their adaption [6,9], to find policies for partially observable systems [11], to analyse Bayesian networks [34], and to speed up the analysis of, e.g., software product lines [10,37]. On top of technical differences, none of these approaches uses a hierarchical decomposition of an MDP or uses the results of the analysis in the analysis of a larger MDP.…”

Section: Related Workmentioning

confidence: 99%

Abstraction-Refinement for Hierarchical Probabilistic Models

Junges

¹

,

Spaan

²

2022

Computer Aided Verification

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Markov decision processes are a ubiquitous formalism for modelling systems with non-deterministic and probabilistic behavior. Verification of these models is subject to the famous state space explosion problem. We alleviate this problem by exploiting a hierarchical structure with repetitive parts. This structure not only occurs naturally in robotics, but also in probabilistic programs describing, e.g., network protocols. Such programs often repeatedly call a subroutine with similar behavior. In this paper, we focus on a local case, in which the subroutines have a limited effect on the overall system state. The key ideas to accelerate analysis of such programs are (1) to treat the behavior of the subroutine as uncertain and only remove this uncertainty by a detailed analysis if needed, and (2) to abstract similar subroutines into a parametric template, and then analyse this template. These two ideas are embedded into an abstraction-refinement loop that analyses hierarchical MDPs. A prototypical implementation shows the efficacy of the approach.

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“…The methods presented in [22,13] exploit a repetitive structure in parametric MCs to accelerate the construction of closed form solutions and are not applicable to MDPs. Parametric models have been used to support the design of systems [8,2] or their adaption [6,9], to find policies for partially observable systems [11], to analyse Bayesian networks [34], and to speed up the analysis of, e.g., software product lines [10,37]. On top of technical differences, none of these approaches uses a hierarchical decomposition of an MDP or uses the results of the analysis in the analysis of a larger MDP.…”

Section: Related Workmentioning

confidence: 99%

Abstraction-Refinement for Hierarchical Probabilistic Models

Junges¹,

Spaan²

2022

Preprint

0

View full text Add to dashboard Cite

Markov decision processes are a ubiquitous formalism for modelling systems with non-deterministic and probabilistic behavior. Verification of these models is subject to the famous state space explosion problem. We alleviate this problem by exploiting a hierarchical structure with repetitive parts. This structure not only occurs naturally in robotics, but also in probabilistic programs describing, e.g., network protocols. Such programs often repeatedly call a subroutine with similar behavior. In this paper, we focus on a local case, in which the subroutines have a limited effect on the overall system state. The key ideas to accelerate analysis of such programs are (1) to treat the behavior of the subroutine as uncertain and only remove this uncertainty by a detailed analysis if needed, and (2) to abstract similar subroutines into a parametric template, and then analyse this template. These two ideas are embedded into an abstraction-refinement loop that analyses hierarchical MDPs. A prototypical implementation shows the efficacy of the approach.

show abstract