Taking It to the Limit: Approximate Reasoning for Markov Processes

Larsen, Kim Guldstrand; Mardare, Radu; Panangaden, Prakash

doi:10.1007/978-3-642-32589-2_59

Cited by 18 publications

(17 citation statements)

References 12 publications

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“…For quantitative notions of model comparison, it has long been argued that exact variants such as ours are too strong because they heavily depend on the choice of the numerical parameters, suggesting approximate notions instead (e.g., [11,13,18,25]). Here we have started to tackle this issue by finding a family of models to which an emulation found with a given choice of parameter carries over.…”

Section: Resultsmentioning

confidence: 99%

Comparing chemical reaction networks: A categorical and algorithmic perspective

Cardelli

Tribastone

Tschaikowski

et al. 2019

Theoretical Computer Science

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We study chemical reaction networks (CRNs) as a kernel language for concurrency models with semantics based on ordinary differential equations. We investigate the problem of comparing two CRNs, i.e., to decide whether the trajectories of a source CRN can be matched by a target CRN under an appropriate choice of initial conditions. Using a categorical framework, we extend and relate model-comparison approaches based on structural (syntactic) and on dynamical (semantic) properties of a CRN, proving their equivalence. Then, we provide an algorithm to compare CRNs, running linearly in time with respect to the cardinality of all possible comparisons. Finally, we apply our results to biological models from the literature.

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Section: Resultsmentioning

confidence: 99%

Comparing chemical reaction networks: A categorical and algorithmic perspective

Cardelli

Tribastone

Tschaikowski

et al. 2019

Theoretical Computer Science

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“…This approach has been taken up by a number of articles in the literature, which have introduced metrics as a means to relate two models. Such metrics have been defined based on logical characterizations [15,19,33], categorical notions [43,44], games [17], normed distances over process trajectories [1,31], as well as distances between probability measures [42].…”

Section: Definition 3 (Approximate Probabilistic Bisimulation)mentioning

confidence: 99%

“…We are of course interested in characterising computationally finite relations, which will be the goal pursued in the next section. Presently, only a few approaches exist to approximate uncountable-space processes with finite-state ones: LMPs [9,11,13,19], (infinite-state) MDPs [33], general Markov chains [29] and stochastic hybrid systems (SHSs) [2,3].…”

Section: Computability Of Approximate Probabilistic Bisimulationsmentioning

confidence: 99%

“…LMP approximations are also investigated in [13] and, building on the basis of [17,23], looked at from a different perspective (that of Markov processes as transformers of functions) in [11]. Along the same lines, [33] considers a novel logical characterisation of notions of bisimulations for Markov decision processes. The relationship between exact bisimulation and (CSL) logic is explored in [18] over a continuous-time version of LMPs.…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic Model Checking of Labelled Markov Processes via Finite Approximate Bisimulations

Abate

Kwiatkowska

Norman

et al. 2014

Lecture Notes in Computer Science

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Abstract. This paper concerns labelled Markov processes (LMPs), probabilistic models over uncountable state spaces originally introduced by Prakash Panangaden and colleagues. Motivated by the practical application of the LMP framework, we study its formal semantics and the relationship to similar models formulated in control theory. We consider notions of (exact and approximate) probabilistic bisimulation over LMPs and, drawing on methods from both formal verification and control theory, propose a simple technique to compute an approximate probabilistic bisimulation of a given LMP, where the resulting abstraction is characterised as a finite-state labelled Markov chain (LMC). This construction enables the application of automated quantitative verification and policy synthesis techniques over the obtained abstract model, which can be used to perform approximate analysis of the concrete LMP. We illustrate this process through a case study of a multi-room heating system that employs the probabilistic model checker PRISM.

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“…have worked with distances for Markov processes e.g. in [4,16,34,37], and van Breugel and Worrell et.al. have developed distances for probabilistic transition systems e.g.…”

Section: Introductionmentioning

confidence: 99%

Generalized Quantitative Analysis of Metric Transition Systems

Fahrenberg

Legay

2013

Programming Languages and Systems

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Abstract. The formalism of metric transition systems, as introduced by de Alfaro, Faella and Stoelinga, is convenient for modeling systems and properties with quantitative information, such as probabilities or time. For a number of applications however, one needs other distances than the point-wise (and possibly discounted) linear and branching distances introduced by de Alfaro et.al. for analyzing quantitative behavior. In this paper, we show a vast generalization of the setting of de Alfaro et.al., to a framework where any of a large number of other useful distances can be applied. Concrete instantiations of our framework hence give e.g. limit-average, discounted-sum, or maximum-lead linear and branching distances; in each instantiation, properties similar to the ones of de Alfaro et.al. hold. In the end, we achieve a framework which is not only suitable for modeling different kinds of quantitative systems and properties, but also for analyzing these by using different application-determined ways of measuring quantitative behavior.

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Taking It to the Limit: Approximate Reasoning for Markov Processes

Cited by 18 publications

References 12 publications

Comparing chemical reaction networks: A categorical and algorithmic perspective

Comparing chemical reaction networks: A categorical and algorithmic perspective

Probabilistic Model Checking of Labelled Markov Processes via Finite Approximate Bisimulations

Generalized Quantitative Analysis of Metric Transition Systems

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