Parameter Synthesis for Parametric Interval Markov Chains

Delahaye, Benoît; Lime, Didier; Petrucci, Laure

doi:10.1007/978-3-662-49122-5_18

Cited by 13 publications

(36 citation statements)

References 24 publications

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“…In order to relate a given IPTA with the PTAs it represents, we use the notion of implementation defined hereafter. This notion is similar to the one defined in the context of (parametric) Interval Markov Chains in [Del15;DLP16]. Remark that a PTA implementing an IPTA needs to conserve the exact same clocks, guards and resets.…”

Section: Syntaxmentioning

confidence: 92%

“…Indeed, the structure of implementations depends on the structure of the zone graph rather than on the structure of the IPTA itself which can be different. Algorithms such as those proposed for deciding consistency of (p)IMCs in [DLP16] therefore cannot be directly adapted to the IPTAs setting as they are dependent on this property.…”

Section: The Consistency Problem For Iptasmentioning

confidence: 99%

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Consistency in Parametric Interval Probabilistic Timed Automata

André

Delahaye

Fournier

2020

Journal of Logical and Algebraic Methods in Programming

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We propose a new abstract formalism for probabilistic timed systems, Parametric Interval Probabilistic Timed Automata, based on an extension of Parametric Timed Automata and Interval Markov Chains. In this context, we consider the consistency problem that amounts to deciding whether a given specification admits at least one implementation. In the context of Interval Probabilistic Timed Automata (with no timing parameters), we show that this problem is decidable and propose a constructive algorithm for its resolution. We show that the existence of timing parameter valuations ensuring consistency is undecidable in the general context, but still exhibit a syntactic condition on parameters to ensure decidability. We also propose procedures that resolve both the consistency and the consistent reachability problems when the parametric probabilistic zone graph is finite.

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Section: Syntaxmentioning

confidence: 92%

Section: The Consistency Problem For Iptasmentioning

confidence: 99%

Consistency in Parametric Interval Probabilistic Timed Automata

André

Delahaye

Fournier

2020

Journal of Logical and Algebraic Methods in Programming

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“…Let Y be a finite set of parameters and v be a valuation over Y . By combining notations used for IMCs and pMCs the set I(Q Y ) contains all parametrized intervals over [0,1], and for all In [9] the authors introduced pIMCs where parametric interval endpoints are limited to linear combination of parameters. In this paper we extend the pIMC model by allowing rational functions over parameters as endpoints of parametric intervals.…”

Section: Existing MC Abstraction Modelsmentioning

confidence: 99%

“…-CSP (X, D, C ∪ s∈Sα ρ s ) is satisfiable iff α is existential reachable in P -CSP (X, D, C ∪ s∈Sα ¬ρ s ) is unsatisfiable iff α is universal reachable in P As for the existential consistency problem, we have an exponential gain in terms of size of the encoding compared to [9]: the number of constraints and variables in C ∃r is linear in terms of the size of the encoded pIMC.…”

Section: Qualitative Reachabilitymentioning

confidence: 99%

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Reachability in Parametric Interval Markov Chains Using Constraints

Bart

Delahaye

Lime

et al. 2017

Quantitative Evaluation of Systems

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Abstract. Parametric Interval Markov Chains (pIMCs) are a specification formalism that extend Markov Chains (MCs) and Interval Markov Chains (IMCs) by taking into account imprecision in the transition probability values: transitions in pIMCs are labeled with parametric intervals of probabilities. In this work, we study the difference between pIMCs and other Markov Chain abstractions models and investigate the two usual semantics for IMCs: once-and-for-all and at-every-step. In particular, we prove that both semantics agree on the maximal/minimal reachability probabilities of a given IMC. We then investigate solutions to several parameter synthesis problems in the context of pIMCs -consistency, qualitative reachability and quantitative reachability -that rely on constraint encodings. Finally, we propose a prototype implementation of our constraint encodings with promising results.

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Reachability in Augmented Interval Markov Chains

Chonev

2019

Lecture Notes in Computer Science

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In this paper we propose augmented interval Markov chains (AIMCs): a generalisation of the familiar interval Markov chains (IMCs) where uncertain transition probabilities are in addition allowed to depend on one another. This new model preserves the flexibility afforded by IMCs for describing stochastic systems where the parameters are unclear, for example due to measurement error, but also allows us to specify transitions with probabilities known to be identical, thereby lending further expressivity.The focus of this paper is reachability in AIMCs. We study the qualitative, exact quantitative and approximate reachability problem, as well as natural subproblems thereof, and establish several upper and lower bounds for their complexity. We prove the exact reachability problem is at least as hard as the famous square-root sum problem, but, encouragingly, the approximate version lies in NP if the underlying graph is known, whilst the restriction of the exact problem to a constant number of uncertain edges is in P. Finally, we show that uncertainty in the graph structure affects complexity by proving NP-completeness for the qualitative subproblem, in contrast with an easily-obtained upper bound of P for the same subproblem with known graph structure.

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Parameter Synthesis for Parametric Interval Markov Chains

Cited by 13 publications

References 24 publications

Consistency in Parametric Interval Probabilistic Timed Automata

Consistency in Parametric Interval Probabilistic Timed Automata

Reachability in Parametric Interval Markov Chains Using Constraints

Reachability in Augmented Interval Markov Chains

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