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Erschienen in:
Automating Abstract Interpretation Kapitel lesen Erstes Kapitel lesen

2016 | OriginalPaper | Buchkapitel

Reward-Bounded Reachability Probability for Uncertain Weighted MDPs

verfasst von : Vahid Hashemi, Holger Hermanns, Lei Song

Erschienen in: Verification, Model Checking, and Abstract Interpretation

Verlag: Springer Berlin Heidelberg

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Abstract

In this paper we present a decision algorithm for computing maximal/minimal reward-bounded reachability probabilities in weighted MDPs with uncertainties. Even though an uncertain weighted MDP (\(\textit{UwMDP}\)) represents an equivalent weighted MDP which may be exponentially larger, our algorithm does not cause an exponentially blow-up and will terminate in polynomial time with respect to the size of \(\textit{UwMDP}\)s. We also define bisimulation relations for \(\textit{UwMDP}\)s, which are compositional and can be decided in polynomial time as well. We develop a prototype tool and apply it to some case studies to show its effectiveness.

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Vorheriges Kapitel Abstraction-driven Concolic Testing
Nächstes Kapitel Parameter Synthesis for Parametric Interval Markov Chains
Fußnoten
1
We only consider integer weights in this paper. The extension to rational weights is straightforward.
 
2
Here, \(\mathcal {B}\) is the standard \(\sigma \)-algebra over \( Paths ^{ inf }_{\mathcal {M}_{\mathcal {U}}}\) generated from the set of all cylinder sets \(\{ Paths _{{\mathcal {M}_{\mathcal {U}}}}^{ \xi } \mid \xi \in Paths ^{ fin }_{\mathcal {M}_{\mathcal {U}}}\}\). The unique probability measure is obtained by the application of the extension theorem (see, e.g. [7]) .
 
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Metadaten
Titel
Reward-Bounded Reachability Probability for Uncertain Weighted MDPs
verfasst von
Vahid Hashemi
Holger Hermanns
Lei Song
Copyright-Jahr
2016
Verlag
Springer Berlin Heidelberg
Buch
Verification, Model Checking, and Abstract Interpretation

Print ISBN: 978-3-662-49121-8

Electronic ISBN: 978-3-662-49122-5

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-3-662-49122-5_17

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