Time-Bounded Model Checking of Infinite-State Continuous-Time Markov Chains

Hahn, Ernst Moritz; Hermanns, Holger; Wachter, Björn; Zhang, Lijun

doi:10.3233/fi-2009-145

Cited by 16 publications

(7 citation statements)

References 37 publications

(90 reference statements)

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“…In a previous publication [15], we have extended these results such that we were able to do approximate model checking for a subset of CSL. This subset excluded the steady-state operator as well as the unbounded until operator.…”

Section: Introductionmentioning

confidence: 82%

“…The techniques of this paper are derived from combinations of our previous works [14,15] and [7,23]. This work has been inspired and is related by a number of other works.…”

Section: Related Workmentioning

confidence: 99%

“…Then, we remove all transitions from the states at the border and set all of their atomic propositions to ?. In previous works [15] we already discussed some variants of such a model exploration. In Subsection 3.1 we give another such technique.…”

Section: Model Checking Based On Truncationsmentioning

confidence: 99%

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Model Checking CSL for Markov Population Models

Spieler

Hahn²,

Zhang³

2014

Electron. Proc. Theor. Comput. Sci.

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Markov population models (MPMs) are a widely used modelling formalism in the area of computational biology and related areas. The semantics of a MPM is an infinite-state continuous-time Markov chain. In this paper, we use the established continuous stochastic logic (CSL) to express properties of Markov population models. This allows us to express important measures of biological systems, such as probabilistic reachability, survivability, oscillations, switching times between attractor regions, and various others. Because of the infinite state space, available analysis techniques only apply to a very restricted subset of CSL properties. We present a full algorithm for model checking CSL for MPMs, and provide experimental evidence showing that our method is effective.Comment: In Proceedings QAPL 2014, arXiv:1406.156

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Section: Introductionmentioning

confidence: 82%

“…The techniques of this paper are derived from combinations of our previous works [14,15] and [7,23]. This work has been inspired and is related by a number of other works.…”

Section: Related Workmentioning

confidence: 99%

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Model Checking CSL for Markov Population Models

Spieler

Hahn²,

Zhang³

2014

Electron. Proc. Theor. Comput. Sci.

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“…More precisely, it was shown that Pr s (ϕ) can be approximated, up to an a priori given precision ε, by a sum of transient probabilities in the CTMCs. Their algorithm then led to further development of approximation algorithms for infinite CTMCs [11,12] and abstraction techniques [15]. More importantly, several tools support approximate model checking, including PRISM [17] and MRMC [16].…”

Section: Introductionmentioning

confidence: 99%

Efficient CSL Model Checking Using Stratification

Zhang

Jansen

Nielson

et al. 2012

Logical Methods in Computer Science

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Abstract. For continuous-time Markov chains, the model-checking problem with respect to continuous-time stochastic logic (CSL) has been introduced and shown to be decidable by Aziz, Sanwal, Singhal and Brayton in 1996 [1, 2]. Their proof can be turned into an approximation algorithm with worse than exponential complexity. In 2000, Baier, Haverkort, Hermanns and Katoen [4,5] presented an efficient polynomial-time approximation algorithm for the sublogic in which only binary until is allowed. In this paper, we propose such an efficient polynomial-time approximation algorithm for full CSL.The key to our method is the notion of stratified CTMCs with respect to the CSL property to be checked. On a stratified CTMC, the probability to satisfy a CSL path formula can be approximated by a transient analysis in polynomial time (using uniformization). We present a measure-preserving, linear-time and -space transformation of any CTMC into an equivalent, stratified one. This makes the present work the centerpiece of a broadly applicable full CSL model checker.Recently, the decision algorithm by Aziz et al. was shown to work only for stratified CTMCs. As an additional contribution, our measure-preserving transformation can be used to ensure the decidability for general CTMCs.

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“…A similar approach is used in[8] to analyse infinite Markov chains. However in[8] after the expansion phase (that is used to compute a finite truncation of the original system), the standard model checking algorithm is used. Indeed, differently from the solution proposed in this paper, satisfaction of Φ 1 and Φ 2 does not play any rôle.…”

mentioning

confidence: 99%

On-the-fly Probabilistic Model Checking

Latella

Loreti

Massink

2014

Electron. Proc. Theor. Comput. Sci.

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Model checking approaches can be divided into two broad categories: global approaches that determine the set of all states in a model M that satisfy a temporal logic formula f, and local approaches in which, given a state s in M, the procedure determines whether s satisfies f. When s is a term of a process language, the model checking procedure can be executed "on-the-fly", driven by the syntactical structure of s. For certain classes of systems, e.g. those composed of many parallel components, the local approach is preferable because, depending on the specific property, it may be sufficient to generate and inspect only a relatively small part of the state space. We propose an efficient, on-the-fly, PCTL model checking procedure that is parametric with respect to the semantic interpretation of the language. The procedure comprises both bounded and unbounded until modalities. The correctness of the procedure is shown and its efficiency is compared with a global PCTL model checker on representative applications.Comment: In Proceedings ICE 2014, arXiv:1410.701

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Time-Bounded Model Checking of Infinite-State Continuous-Time Markov Chains

Cited by 16 publications

References 37 publications

Model Checking CSL for Markov Population Models

Model Checking CSL for Markov Population Models

Efficient CSL Model Checking Using Stratification

On-the-fly Probabilistic Model Checking

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