Approximate Model Checking of Stochastic Hybrid Systems

Abate, Alessandro; Katoen, Joost-Pieter; Lygeros, John; Prandini, Maria

doi:10.3166/ejc.16.624-641

Cited by 167 publications

(236 citation statements)

References 30 publications

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“…⊓ Example 2 (Decision process). Let us consider a variant of the temperature control model presented in [3,5] and which will be further elaborated upon in Section 6. The temperature of a room is controlled at the discrete time instants t k = 0, δ, 2δ, .…”

Section: Definition 1 (Labelled Markov Process) a Labelled Markov Prmentioning

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%

“…The abstraction procedure is based on a discretisation of the state space of the LMP (recall that the space of labels (actions) is finite and as such requires no discretisation) and is inspired by the early work in [3] over (fully-probabilistic) SHS models. It is now extended to account for the presence of actions and to accommodate the LMP framework (with sub-probability measures).…”

Section: From Lmps To Finite Labelled Markov Chainsmentioning

confidence: 99%

“…Of particular interest is the result that quantitative finite abstractions of uncountable-space stochastic processes [2,3] are related to the original, uncountable-state models by notions of approximate probabilistic bisimulations [41]. These notions are characterised via distances between probability measures.…”

Section: Introductionmentioning

confidence: 99%

“…Abstractions that are related to Panangaden's finite-state approximants are studied over PCTL properties in [29]. In control theory, the goal of [2,3] is to enable the verification of step-bounded PCTL-like properties [21], as well as time-bounded [41] or unbounded [40] linear-temporal specifications. It is then shown that these approximations are related to the original, uncountable-state models by notions of approximate probabilistic bisimulations [41].…”

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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Section: Definition 1 (Labelled Markov Process) a Labelled Markov Prmentioning

confidence: 99%