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Joost-pieter Katoen - One of the best experts on this subject based on the ideXlab platform.
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On the Complexity of Reachability in Parametric Markov Decision Processes
arXiv: Logic in Computer Science, 2019Co-Authors: Tobias Winkler, Sebastian Junges, Guillermo A. Pérez, Joost-pieter KatoenAbstract: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. Fixing values for all parameters yields MDPs. In particular, this paper studies the complexity of finding values for these parameters such that the induced MDP satisfies some reachability constraints. We discuss different variants depending on the Comparison Operator in the constraints and the domain of the parameter values. We improve all known lower bounds for this problem, and notably provide ETR-completeness results for distinct variants of this problem. Furthermore, we provide insights in the functions describing the induced reachability probabilities, and how pMDPs generalise concurrent stochastic reachability games.
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CONCUR - On the Complexity of Reachability in Parametric Markov Decision Processes
2019Co-Authors: Tobias Winkler, Sebastian Junges, Guillermo A. Pérez, Joost-pieter KatoenAbstract: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. Fixing values for all parameters yields MDPs. In particular, this paper studies the complexity of finding values for these parameters such that the induced MDP satisfies some reachability constraints. We discuss different variants depending on the Comparison Operator in the constraints and the domain of the parameter values. We improve all known lower bounds for this problem, and notably provide ETR-completeness results for distinct variants of this problem. Furthermore, we provide insights in the functions describing the induced reachability probabilities, and how pMDPs generalise concurrent stochastic reachability games.
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model checking continuous time markov chains by transient analysis
Computer Aided Verification, 2000Co-Authors: Christel Baier, Boudewijn R Haverkort, Holger Hermanns, Joost-pieter KatoenAbstract:The verification of continuous-time Markov chains (CTMCs) against continuous stochastic logic (CSL) [3,6], a stochastic branching-time temporal logic, is considered. CSL facilitates among others the specification of steady-state properties and the specification of probabilistic timing properties of the form \({\cal P}_{\bowtie p}(\Phi_1 \, {\cal U}^{I} \, \Phi_2)\), for state formulas Φ1 and Φ2, Comparison Operator ⋈, probability p, and real interval I. The main result of this paper is that model checking probabilistic timing properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows us to verify such properties by using efficient techniques for transient analysis of CTMCs such as uniformisation. A second result is that a variant of ordinary lumping equivalence (i.e., bisimulation), a well-known notion for aggregating CTMCs, preserves the validity of all CSL-formulas.
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model checking continuous time markov chains by transient analysis
Lecture Notes in Computer Science, 2000Co-Authors: Christel Baier, Boudewijn R Haverkort, Holger Hermanns, Joost-pieter KatoenAbstract:The verification of continuous-time Markov chains (CTMCs) against continuous stochastic logic (CSL) [3,6], a stochastic branching-time temporal logic, is considered. CSL facilitates among others the specification of steady-state properties and the specification of probabilistic timing properties of the form P ?P (Φ 1 u I Φ 2 ), for state formulas Φ 1 and Φ 2 , Comparison Operator?, probability p, and real interval I. The main result of this paper is that model checking probabilistic timing properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows us to verify such properties by using efficient techniques for transient analysis of CTMCs such as uniformisation. A second result is that a variant of ordinary lumping equivalence (i.e., bisimulation), a well-known notion for aggregating CTMCs, preserves the validity of all CSL-formulas.
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CAV - Model Checking Continuous-Time Markov Chains by Transient Analysis
Computer Aided Verification, 2000Co-Authors: Christel Baier, Boudewijn R Haverkort, Holger Hermanns, Joost-pieter KatoenAbstract:The verification of continuous-time Markov chains (CTMCs) against continuous stochastic logic (CSL) [3,6], a stochastic branching-time temporal logic, is considered. CSL facilitates among others the specification of steady-state properties and the specification of probabilistic timing properties of the form \({\cal P}_{\bowtie p}(\Phi_1 \, {\cal U}^{I} \, \Phi_2)\), for state formulas Φ1 and Φ2, Comparison Operator ⋈, probability p, and real interval I. The main result of this paper is that model checking probabilistic timing properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows us to verify such properties by using efficient techniques for transient analysis of CTMCs such as uniformisation. A second result is that a variant of ordinary lumping equivalence (i.e., bisimulation), a well-known notion for aggregating CTMCs, preserves the validity of all CSL-formulas.
Christel Baier - One of the best experts on this subject based on the ideXlab platform.
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model checking continuous time markov chains by transient analysis
Computer Aided Verification, 2000Co-Authors: Christel Baier, Boudewijn R Haverkort, Holger Hermanns, Joost-pieter KatoenAbstract:The verification of continuous-time Markov chains (CTMCs) against continuous stochastic logic (CSL) [3,6], a stochastic branching-time temporal logic, is considered. CSL facilitates among others the specification of steady-state properties and the specification of probabilistic timing properties of the form \({\cal P}_{\bowtie p}(\Phi_1 \, {\cal U}^{I} \, \Phi_2)\), for state formulas Φ1 and Φ2, Comparison Operator ⋈, probability p, and real interval I. The main result of this paper is that model checking probabilistic timing properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows us to verify such properties by using efficient techniques for transient analysis of CTMCs such as uniformisation. A second result is that a variant of ordinary lumping equivalence (i.e., bisimulation), a well-known notion for aggregating CTMCs, preserves the validity of all CSL-formulas.
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model checking continuous time markov chains by transient analysis
Lecture Notes in Computer Science, 2000Co-Authors: Christel Baier, Boudewijn R Haverkort, Holger Hermanns, Joost-pieter KatoenAbstract:The verification of continuous-time Markov chains (CTMCs) against continuous stochastic logic (CSL) [3,6], a stochastic branching-time temporal logic, is considered. CSL facilitates among others the specification of steady-state properties and the specification of probabilistic timing properties of the form P ?P (Φ 1 u I Φ 2 ), for state formulas Φ 1 and Φ 2 , Comparison Operator?, probability p, and real interval I. The main result of this paper is that model checking probabilistic timing properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows us to verify such properties by using efficient techniques for transient analysis of CTMCs such as uniformisation. A second result is that a variant of ordinary lumping equivalence (i.e., bisimulation), a well-known notion for aggregating CTMCs, preserves the validity of all CSL-formulas.
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CAV - Model Checking Continuous-Time Markov Chains by Transient Analysis
Computer Aided Verification, 2000Co-Authors: Christel Baier, Boudewijn R Haverkort, Holger Hermanns, Joost-pieter KatoenAbstract:The verification of continuous-time Markov chains (CTMCs) against continuous stochastic logic (CSL) [3,6], a stochastic branching-time temporal logic, is considered. CSL facilitates among others the specification of steady-state properties and the specification of probabilistic timing properties of the form \({\cal P}_{\bowtie p}(\Phi_1 \, {\cal U}^{I} \, \Phi_2)\), for state formulas Φ1 and Φ2, Comparison Operator ⋈, probability p, and real interval I. The main result of this paper is that model checking probabilistic timing properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows us to verify such properties by using efficient techniques for transient analysis of CTMCs such as uniformisation. A second result is that a variant of ordinary lumping equivalence (i.e., bisimulation), a well-known notion for aggregating CTMCs, preserves the validity of all CSL-formulas.
Boudewijn R Haverkort - One of the best experts on this subject based on the ideXlab platform.
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model checking continuous time markov chains by transient analysis
Computer Aided Verification, 2000Co-Authors: Christel Baier, Boudewijn R Haverkort, Holger Hermanns, Joost-pieter KatoenAbstract:The verification of continuous-time Markov chains (CTMCs) against continuous stochastic logic (CSL) [3,6], a stochastic branching-time temporal logic, is considered. CSL facilitates among others the specification of steady-state properties and the specification of probabilistic timing properties of the form \({\cal P}_{\bowtie p}(\Phi_1 \, {\cal U}^{I} \, \Phi_2)\), for state formulas Φ1 and Φ2, Comparison Operator ⋈, probability p, and real interval I. The main result of this paper is that model checking probabilistic timing properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows us to verify such properties by using efficient techniques for transient analysis of CTMCs such as uniformisation. A second result is that a variant of ordinary lumping equivalence (i.e., bisimulation), a well-known notion for aggregating CTMCs, preserves the validity of all CSL-formulas.
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model checking continuous time markov chains by transient analysis
Lecture Notes in Computer Science, 2000Co-Authors: Christel Baier, Boudewijn R Haverkort, Holger Hermanns, Joost-pieter KatoenAbstract:The verification of continuous-time Markov chains (CTMCs) against continuous stochastic logic (CSL) [3,6], a stochastic branching-time temporal logic, is considered. CSL facilitates among others the specification of steady-state properties and the specification of probabilistic timing properties of the form P ?P (Φ 1 u I Φ 2 ), for state formulas Φ 1 and Φ 2 , Comparison Operator?, probability p, and real interval I. The main result of this paper is that model checking probabilistic timing properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows us to verify such properties by using efficient techniques for transient analysis of CTMCs such as uniformisation. A second result is that a variant of ordinary lumping equivalence (i.e., bisimulation), a well-known notion for aggregating CTMCs, preserves the validity of all CSL-formulas.
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CAV - Model Checking Continuous-Time Markov Chains by Transient Analysis
Computer Aided Verification, 2000Co-Authors: Christel Baier, Boudewijn R Haverkort, Holger Hermanns, Joost-pieter KatoenAbstract:The verification of continuous-time Markov chains (CTMCs) against continuous stochastic logic (CSL) [3,6], a stochastic branching-time temporal logic, is considered. CSL facilitates among others the specification of steady-state properties and the specification of probabilistic timing properties of the form \({\cal P}_{\bowtie p}(\Phi_1 \, {\cal U}^{I} \, \Phi_2)\), for state formulas Φ1 and Φ2, Comparison Operator ⋈, probability p, and real interval I. The main result of this paper is that model checking probabilistic timing properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows us to verify such properties by using efficient techniques for transient analysis of CTMCs such as uniformisation. A second result is that a variant of ordinary lumping equivalence (i.e., bisimulation), a well-known notion for aggregating CTMCs, preserves the validity of all CSL-formulas.
Holger Hermanns - One of the best experts on this subject based on the ideXlab platform.
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model checking continuous time markov chains by transient analysis
Computer Aided Verification, 2000Co-Authors: Christel Baier, Boudewijn R Haverkort, Holger Hermanns, Joost-pieter KatoenAbstract:The verification of continuous-time Markov chains (CTMCs) against continuous stochastic logic (CSL) [3,6], a stochastic branching-time temporal logic, is considered. CSL facilitates among others the specification of steady-state properties and the specification of probabilistic timing properties of the form \({\cal P}_{\bowtie p}(\Phi_1 \, {\cal U}^{I} \, \Phi_2)\), for state formulas Φ1 and Φ2, Comparison Operator ⋈, probability p, and real interval I. The main result of this paper is that model checking probabilistic timing properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows us to verify such properties by using efficient techniques for transient analysis of CTMCs such as uniformisation. A second result is that a variant of ordinary lumping equivalence (i.e., bisimulation), a well-known notion for aggregating CTMCs, preserves the validity of all CSL-formulas.
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model checking continuous time markov chains by transient analysis
Lecture Notes in Computer Science, 2000Co-Authors: Christel Baier, Boudewijn R Haverkort, Holger Hermanns, Joost-pieter KatoenAbstract:The verification of continuous-time Markov chains (CTMCs) against continuous stochastic logic (CSL) [3,6], a stochastic branching-time temporal logic, is considered. CSL facilitates among others the specification of steady-state properties and the specification of probabilistic timing properties of the form P ?P (Φ 1 u I Φ 2 ), for state formulas Φ 1 and Φ 2 , Comparison Operator?, probability p, and real interval I. The main result of this paper is that model checking probabilistic timing properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows us to verify such properties by using efficient techniques for transient analysis of CTMCs such as uniformisation. A second result is that a variant of ordinary lumping equivalence (i.e., bisimulation), a well-known notion for aggregating CTMCs, preserves the validity of all CSL-formulas.
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CAV - Model Checking Continuous-Time Markov Chains by Transient Analysis
Computer Aided Verification, 2000Co-Authors: Christel Baier, Boudewijn R Haverkort, Holger Hermanns, Joost-pieter KatoenAbstract:The verification of continuous-time Markov chains (CTMCs) against continuous stochastic logic (CSL) [3,6], a stochastic branching-time temporal logic, is considered. CSL facilitates among others the specification of steady-state properties and the specification of probabilistic timing properties of the form \({\cal P}_{\bowtie p}(\Phi_1 \, {\cal U}^{I} \, \Phi_2)\), for state formulas Φ1 and Φ2, Comparison Operator ⋈, probability p, and real interval I. The main result of this paper is that model checking probabilistic timing properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows us to verify such properties by using efficient techniques for transient analysis of CTMCs such as uniformisation. A second result is that a variant of ordinary lumping equivalence (i.e., bisimulation), a well-known notion for aggregating CTMCs, preserves the validity of all CSL-formulas.
Pavel Exner - One of the best experts on this subject based on the ideXlab platform.
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On the Dense Point and Absolutely Continuous Spectrum for Hamiltonians with Concentric δ Shells
Letters in Mathematical Physics, 2007Co-Authors: Pavel Exner, Martin FraasAbstract:We consider Schrödinger Operators in dimension ν ≥ 2 with a singular interaction supported by an infinite family of concentric spheres, analogous to a system studied by Hempel and coauthors for regular potentials. The essential spectrum covers a half line determined by the appropriate one-dimensional Comparison Operator; it is dense pure point in the gaps of the latter. If the interaction is nontrivial and radially periodic, there are infinitely many absolutely continuous bands; in contrast to the regular case the lengths of the p.p. segments interlacing with the bands tend asymptotically to a positive constant in the high-energy limit.
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Spectral properties of Schroedinger Operators with a strongly attractive delta interaction supported by a surface
arXiv: Mathematical Physics, 2003Co-Authors: Pavel ExnerAbstract:We investigate the Operator $-\Delta -\alpha \delta (x-\Gamma)$ in $L^2(\mathbb{R}^3)$, where $\Gamma$ is a smooth surface which is either compact or periodic and satisfies suitable regularity requirements. We find an asymptotic expansion for the lower part of the spectrum as $\alpha\to\infty$ which involves a ``two-dimensional'' Comparison Operator determined by the geometry of the surface $\Gamma$. In the compact case the asymptotics concerns negative eigenvalues, in the periodic case Floquet eigenvalues. We also give a bandwidth estimate in the case when a periodic $\Gamma$ decomposes into compact connected components. Finally, we comment on analogous systems of lower dimension and other aspects of the problem.
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Bound states due to a strong δ interaction supported by a curved surface
Journal of Physics A: Mathematical and General, 2002Co-Authors: Pavel Exner, Sylwia KondejAbstract:We study the Schrodinger Operator −Δ − αδ(x − Γ) in L2(3) with a δ interaction supported by an infinite non-planar surface Γ which is smooth and admits a global normal parametrization with a uniformly elliptic metric. We show that if Γ is asymptotically planar in a suitable sense and α > 0 is sufficiently large, this Operator has a non-empty discrete spectrum and derive an asymptotic expansion of the eigenvalues in terms of a 'two-dimensional' Comparison Operator determined by the geometry of the surface Γ.