Parametric Markov chains: PCTL complexity and fraction-free Gaussian elimination

Baier, Christel; Hensel, Christian; Hutschenreiter, Lisa; Junges, Sebastian; Katoen, Joost-Pieter; Klein, Joachim

doi:10.1016/j.ic.2019.104504

Cited by 34 publications

(41 citation statements)

References 11 publications

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“…Symbolic probabilistic model checking also scales badly on some models where A has a concise encoding but x has too many different entries. 5 Therefore, model checkers may store x partially explicit [49].…”

Section: A Model Checking Perspectivementioning

confidence: 99%

“…For bounded reachability (or acyclic pMCs), this function amounts to a sum over all paths with every path reflected by a term of a polynomial, i.e., the sum is a polynomial. In sum-of-terms representation, the polynomial can be exponential in the number of parameters [5]. For computational efficiency, we need a smaller representation of the CT. As we only consider reachability of T , we may simplify [43] the notion of (weak) bisimulation [6] (in the formulation of [40]) to the following definition.…”

Section: Operational Perspectivementioning

confidence: 99%

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Model Checking Finite-Horizon Markov Chains with Probabilistic Inference

Holtzen

Junges

Vazquez-Chanlatte

et al. 2021

Lecture Notes in Computer Science

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We revisit the symbolic verification of Markov chains with respect to finite horizon reachability properties. The prevalent approach iteratively computes step-bounded state reachability probabilities. By contrast, recent advances in probabilistic inference suggest symbolically representing all horizon-length paths through the Markov chain. We ask whether this perspective advances the state-of-the-art in probabilistic model checking. First, we formally describe both approaches in order to highlight their key differences. Then, using these insights we develop Rubicon, a tool that transpiles Prism models to the probabilistic inference tool . Finally, we demonstrate better scalability compared to probabilistic model checkers on selected benchmarks. All together, our results suggest that probabilistic inference is a valuable addition to the probabilistic model checking portfolio, with Rubicon as a first step towards integrating both perspectives.

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Section: A Model Checking Perspectivementioning

confidence: 99%

Section: Operational Perspectivementioning

confidence: 99%

Model Checking Finite-Horizon Markov Chains with Probabilistic Inference

Holtzen

Junges

Vazquez-Chanlatte

et al. 2021

Lecture Notes in Computer Science

Self Cite

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“…The most promising techniques are based on parameter lifting that treats identical parameters in different transitions independently [8,36] and has been implemented in the state-of-the-art probabilistic model checkers Storm [18] and PRISM [27]. An alternative approach based on building rational functions for the satisfaction probability has been proposed in [15] and further improved in [22,17,4]. This approach has been also applied to different problems such as model repair [5,34,11].…”

Section: Related Workmentioning

confidence: 99%

Inductive Synthesis for Probabilistic Programs Reaches New Horizons

Andriushchenko

Češka

Junges

et al. 2021

Tools and Algorithms for the Construction and Analysis of Systems

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This paper presents a novel method for the automated synthesis of probabilistic programs. The starting point is a program sketch representing a finite family of finite-state Markov chains with related but distinct topologies, and a reachability specification. The method builds on a novel inductive oracle that greedily generates counter-examples (CEs) for violating programs and uses them to prune the family. These CEs leverage the semantics of the family in the form of bounds on its best- and worst-case behaviour provided by a deductive oracle using an MDP abstraction. The method further monitors the performance of the synthesis and adaptively switches between inductive and deductive reasoning. Our experiments demonstrate that the novel CE construction provides a significantly faster and more effective pruning strategy leading to an accelerated synthesis process on a wide range of benchmarks. For challenging problems, such as the synthesis of decentralized partially-observable controllers, we reduce the run-time from a day to minutes.

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“…This is the case, for instance, when agents in a MAS (partially) ignore the stochastic behaviour of other agents in the system. A possible way to overcome this limitation is represented by socalled parametric Markov models [2,10], which replace precise probabilities with unknown parameters. In [2] for instance, the authors introduce an extension of PCTL specific for parametric Markov chains.…”

Section: Introductionmentioning

confidence: 99%

Logic and Model Checking by Imprecise Probabilistic Interpreted Systems

Termine

Antonucci

Primiero

et al. 2021

Lecture Notes in Computer Science

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Stochastic multi-agent systems raise the necessity to extend probabilistic model checking to the epistemic domain. Results in this direction have been achieved by epistemic extensions of Probabilistic Computation Tree Logic and related Probabilistic Interpreted Systems. The latter, however, suffer of an important limitation: they require the probabilities governing the system's behaviour to be fully specified. A promising way to overcome this limitation is represented by imprecise probabilities. In this paper we introduce imprecise probabilistic interpreted systems and present a related logical language and model-checking procedures based on recent advances in the study of imprecise Markov processes.

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Parametric Markov chains: PCTL complexity and fraction-free Gaussian elimination

Cited by 34 publications

References 11 publications

Model Checking Finite-Horizon Markov Chains with Probabilistic Inference

Model Checking Finite-Horizon Markov Chains with Probabilistic Inference

Inductive Synthesis for Probabilistic Programs Reaches New Horizons

Logic and Model Checking by Imprecise Probabilistic Interpreted Systems

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