A Symbolic Algorithm for Optimal Markov Chain Lumping

Derisavi, S.

doi:10.1007/978-3-540-71209-1_13

Cited by 23 publications

(13 citation statements)

References 16 publications

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“…Recent studies, however, have shown this approach to be of benefit for CSL model checking on a range of different models [29]. A new algorithm, based on the same efficient, symbolic data structures that are used in the PRISM model checker, was presented in [30]. An additional benefit of bisimulation reduction techniques is that they can be applied compositionally [31], i.e.…”

Section: Exact Reduction Techniquesmentioning

confidence: 97%

Probabilistic model checking of complex biological pathways

Heath

Kwiatkowska

Norman

et al. 2008

Theoretical Computer Science

133

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Probabilistic model checking is a formal verification technique that has been successfully applied to the analysis of systems from a broad range of domains, including security and communication protocols, distributed algorithms and power management. In this paper we illustrate its applicability to a complex biological system: the FGF (Fibroblast Growth Factor) signalling pathway. We give a detailed description of how this case study can be modelled in the probabilistic model checker PRISM, discussing some of the issues that arise in doing so, and show how we can thus examine a rich selection of quantitative properties of this model. We present experimental results for the case study under several different scenarios and provide a detailed analysis, illustrating how this approach can be used to yield a better understanding of the dynamics of the pathway. Finally, we outline a number of exact and approximate techniques to enable the verification of larger and more complex pathways and apply several of them to the FGF case study.

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Section: Exact Reduction Techniquesmentioning

confidence: 97%

Probabilistic model checking of complex biological pathways

Heath

Kwiatkowska

Norman

et al. 2008

Theoretical Computer Science

133

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“…We aso plan to investigate the integration of more advanced symbolic representations of state space partitions, such as [12].…”

Section: Resultsmentioning

confidence: 99%

Symbolic Magnifying Lens Abstraction in Markov Decision Processes

Roy

Parker

Norman

et al. 2008

2008 Fifth International Conference on Quantitative Evaluation of Systems

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“…Efficient and optimal algorithms for lumping CTMCs are presented in (Baarir et al 2011) that simplifies the previous work of Derisavi et al (2003); here, the symmetries of the CTMCs underlying complex models are exploited to carry out a reduction of the state space using different notions of lumping. A symbolic approach to algorithmic lumping is taken in (Derisavi 2007), while in (Derisavi et al 2004) the authors show how to derive the lumped Markov chain of very large models by means of a hierarchical inspection based on some shared state variables. The properties of lumping with respect to temporal logics are studied in (Baier et al 2003).…”

Section: Related Workmentioning

confidence: 99%

Lumping and reversed processes in cooperating automata

2014

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Performance evaluation of computer software or hardware architectures may rely on the analysis of a complex stochastic model whose specification is usually given in terms of a high level formalism such as queueing networks, stochastic Petri nets, stochastic automata or Markovian process algebras. Compositionality is a key-feature of many of these formalisms and allows the modeller to combine several (simple) components to form a complex architecture. However, although these formalisms lead to relative compact specifications of possibly complex models, the derivation of the performance indices may be computationally very time and space consuming since the set of possible states of the model tends to grow exponentially (or even faster) with the number of components. In this paper we focus on models with underlying continuous time Markov chains (CTMCs) and we introduce a notion of typed lumpability, which gives sufficient conditions under which a lumping of the process can be derived, allowing the exact computation of marginal stationary probabilities of the cooperating components. The peculiarity of our method relies on the fact that lumping is applied at the component-level rather than to the CTMC underlying the joint process, thus reducing both the memory requirements and the computational cost of the subsequent solution of the model. Moreover, we investigate the properties of the lumping of reversed automata and we prove that, if these are reversible, a conditional product-form solution of their cooperation with other non-blocking automata can be derived. Although conditional product-forms have been previously investigated by other authors with the aim of approximating non-product-form models, the contribution of this paper consists in giving sufficient conditions for this approach to yield exact results and providing examples to support the modeller’s intuition

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A Symbolic Algorithm for Optimal Markov Chain Lumping

Cited by 23 publications

References 16 publications

Probabilistic model checking of complex biological pathways

Probabilistic model checking of complex biological pathways

Symbolic Magnifying Lens Abstraction in Markov Decision Processes

Lumping and reversed processes in cooperating automata

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