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Reachability in Parametric Interval Markov Chains using Constraints [article]

Anicet Bart, Eric Monfroy
2017 arXiv   pre-print
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.  ...  Parametric Interval Markov Chains, as introduced in [9] , abstract IMCs by allowing (combinations of) parameters to be used as interval endpoints in IMCs.  ... 
arXiv:1706.00270v1 fatcat:3gt574xbxbhirkumypfoa47sey

Reachability in Parametric Interval Markov Chains Using Constraints [chapter]

Anicet Bart, Benoît Delahaye, Didier Lime, Éric Monfroy, Charlotte Truchet
2017 Lecture Notes in Computer Science  
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.  ...  Parametric Interval Markov Chains, as introduced in [11] , abstract IMCs by allowing (combinations of) parameters to be used as interval endpoints in IMCs.  ... 
doi:10.1007/978-3-319-66335-7_11 fatcat:4hxd6dscobewxmszkmg5mkrxpq

Reachability in parametric Interval Markov Chains using constraints

Anicet Bart, Benoît Delahaye, Paulin Fournier, Didier Lime, Éric Monfroy, Charlotte Truchet
2018 Theoretical Computer Science  
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.  ...  Parametric Interval Markov Chains, as introduced in [9] , abstract IMCs by allowing (combinations of) parameters to be used as interval endpoints in IMCs.  ... 
doi:10.1016/j.tcs.2018.06.016 fatcat:7tlcirehbzbihccomofo4joobu

Parameter Synthesis for Parametric Interval Markov Chains [chapter]

Benoît Delahaye, Didier Lime, Laure Petrucci
2015 Lecture Notes in Computer Science  
In this paper we study parameter synthesis for a parametric extension of Interval Markov Chains in which the endpoints of intervals may be replaced with parameters.  ...  Interval Markov Chains (IMCs) are the base of a classic probabilistic specification theory introduced by Larsen and Jonsson in 1991. They are also a popular abstraction for probabilistic systems.  ...  Intuitively, pIMCs extend IMCs by allowing parameters to be used as interval endpoints. Definition 4 (Parametric Interval Markov Chain).  ... 
doi:10.1007/978-3-662-49122-5_18 fatcat:l73s4k7g3vc67gjs3dahudg7dq

Parametric Markov Chains: PCTL Complexity and Fraction-free Gaussian Elimination

Lisa Hutschenreiter, Christel Baier, Joachim Klein
2017 Electronic Proceedings in Theoretical Computer Science  
Our contribution to (1) is to show that existing implementations for computing rational functions for reachability probabilities or expected costs in parametric Markov chains can be improved by using fraction-free  ...  Parametric Markov chains have been introduced as a model for families of stochastic systems that rely on the same graph structure, but differ in the concrete transition probabilities.  ...  Interval Markov chain.  ... 
doi:10.4204/eptcs.256.2 fatcat:sjnjfdlicjembfcymvrmn4hs5y

Consistency for Parametric Interval Markov Chains

Benoît Delahaye, Marc Herbstritt
2015 International Workshop on Synthesis of Complex Parameters  
In this paper we introduce and study an extension of Interval Markov Chains with parametric intervals.  ...  Interval Markov Chains (IMCs) are the base of a classic probabilistic specification theory by Larsen and Jonsson in 1991. They are also a popular abstraction for probabilistic systems.  ...  Concluding remarks In this paper, we have introduced the new formalism of parametric Interval Markov Chains, that extends Interval Markov Chains by allowing the use of parameters as lower or upper bounds  ... 
doi:10.4230/oasics.syncop.2015.17 dblp:conf/syncop/Delahaye15 fatcat:ybluqeeg5fb3hltsnghryz6aay

Consistency in Parametric Interval Probabilistic Timed Automata

Étienne André, Benoît Delahaye, Paulin Fournier
2019 Journal of Logical and Algebraic Methods in Programming  
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.  ...  We also propose procedures that resolve both the consistency and the consistent reachability problems when the parametric probabilistic zone graph is finite.  ...  This notion is similar to the one defined in the context of (parametric) Interval Markov Chains [11] , [12] .  ... 
doi:10.1016/j.jlamp.2019.04.007 fatcat:3injmbg2trc35djzurzucszste

The complexity of reachability in parametric Markov decision processes

Sebastian Junges, Joost-Pieter Katoen, Guillermo A. Pérez, Tobias Winkler
2021 Journal of computer and system sciences (Print)  
In particular, this paper studies the complexity of finding values for these parameters such that the induced MDP satisfies some reachability constraints.  ...  This paper studies parametric Markov decision processes (pMDPs), an extension to Markov decision processes (MDPs) where transitions probabilities are described by polynomials over a finite set of parameters  ...  A complete construction is given in [36] . C O N C U R 2 0 1 9 14:4 On the Complexity of Reachability in Parametric Markov Decision Processes Reachability, schedulers and induced Markov chains.  ... 
doi:10.1016/j.jcss.2021.02.006 fatcat:xtg7p2yv5nh5zl2ba6a3sxrp24

Synthesis for PCTL in Parametric Markov Decision Processes [chapter]

Ernst Moritz Hahn, Tingting Han, Lijun Zhang
2011 Lecture Notes in Computer Science  
Daws has devised a language-theoretic approach to solve the reachability problem in parametric Markov chains [11] .  ...  In this context, we are interested in, for instance, determining the parametric reachability probability with respect to a given set of states. This probability is a function in x.  ...  The notion of schedulers is used to resolve nondeterminism, leading to a parametric Markov chain.  ... 
doi:10.1007/978-3-642-20398-5_12 fatcat:owj32dzmv5gnzag5xbwpxs6nzy

Parameter Synthesis Algorithms for Parametric Interval Markov Chains [chapter]

Laure Petrucci, Jaco van de Pol
2018 Lecture Notes in Computer Science  
This paper considers the consistency problem for Parametric Interval Markov Chains.  ...  For parameter synthesis, we use Constraint Logic Programming and the PARMA library for convex polyhedra. 1  ...  Parametric Interval Markov Chains As Parametric Interval Markov Chains allow for describing a family of Markov Chains, we first define these.  ... 
doi:10.1007/978-3-319-92612-4_7 fatcat:2k754m6janhgrdcjbowld7kcci

Fine-Tuning the Odds in Bayesian Networks [article]

Bahare Salmani, Joost-Pieter Katoen
2021 arXiv   pre-print
The key idea is to exploit scalable and powerful techniques for synthesis problems in parametric Markov chains.  ...  ., by restricting the number of parametrized CPTs to one or two, or by avoiding parameter dependencies between several CPTs, in existing works for parametric Bayes networks (pBNs).  ...  Fine-Tuning the Odds in Bayesian Networks  ... 
arXiv:2105.14371v2 fatcat:747gmzhml5fxbdk4zrtzw35qii

FACT: A Probabilistic Model Checker for Formal Verification with Confidence Intervals [chapter]

Radu Calinescu, Kenneth Johnson, Colin Paterson
2016 Lecture Notes in Computer Science  
We introduce FACT, a probabilistic model checker that computes confidence intervals for the evaluated properties of Markov chains with unknown transition probabilities when observations of these transitions  ...  As such, FACT can prevent invalid decisions in the construction and analysis of systems, and extends the applicability of quantitative verification to domains in which unknown estimation errors are unacceptable  ...  This constraint is satisfied by a broad class of PMCs that includes, for instance, all the models used in the case studies of the PROPhESY tool 4 [5] for analysing parametric Markov chains.  ... 
doi:10.1007/978-3-662-49674-9_32 fatcat:3eml6tjviff5tk6oqr5iwycx5y

Scenario-Based Verification of Uncertain MDPs [article]

Murat Cubuktepe, Nils Jansen, Sebastian Junges, Joost-Pieter Katoen, Ufuk Topcu
2020 arXiv   pre-print
We consider Markov decision processes (MDPs) in which the transition probabilities and rewards belong to an uncertainty set parametrized by a collection of random variables.  ...  In general, this problem is undecidable, and we resort to techniques from so-called scenario optimization.  ...  In the future, we plan to exploit our approaches for more involved models such as parametric extensions to continuous-time Markov chains [9] or Markov automata [22] .  ... 
arXiv:1912.11223v2 fatcat:u2p2b4kwczce7higtuo72uqvuy

Scenario-Based Verification of Uncertain MDPs [chapter]

Murat Cubuktepe, Nils Jansen, Sebastian Junges, Joost-Pieter Katoen, Ufuk Topcu
2020 Lecture Notes in Computer Science  
We consider Markov decision processes (MDPs) in which the transition probabilities and rewards belong to an uncertainty set parametrized by a collection of random variables.  ...  In general, this problem is undecidable, and we resort to techniques from so-called scenario optimization.  ...  In the future, we plan to exploit our approaches for more involved models such as parametric extensions to continuous-time Markov chains [9] or Markov automata [22] .  ... 
doi:10.1007/978-3-030-45190-5_16 pmid:32754724 pmcid:PMC7402411 fatcat:n3goluiytjbedhpseq5vpqscfa

Parameter Synthesis for Markov Models [article]

Sebastian Junges, Erika Abraham, Christian Hensel, Nils Jansen, Joost-Pieter Katoen, Tim Quatmann, Matthias Volk
2019 arXiv   pre-print
Markov chain analysis is a key technique in reliability engineering. A practical obstacle is that all probabilities in Markov models need to be known.  ...  This paper presents various analysis algorithms for parametric Markov chains and Markov decision processes. We focus on three problems: (a) do all parameter values within a given region satisfy φ?  ...  ACKNOWLEDGMENT The authors would like to thank Harold Bruintjes and Florian Corzilius for their contributions to PROPhESY 1.0, Tom Janson and Lutz Klinkenberg for their help in developing PROPhESY 2.0,  ... 
arXiv:1903.07993v1 fatcat:nfxcd5lt7jbdni4ika72fnjgme
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