2021
DOI: 10.1007/978-3-030-72016-2_10
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Finding Provably Optimal Markov Chains

Abstract: Parametric Markov chains (pMCs) are Markov chains with symbolic (aka: parametric) transition probabilities. They are a convenient operational model to treat robustness against uncertainties. A typical objective is to find the parameter values that maximize the reachability of some target states. In this paper, we consider automatically proving robustness, that is, an $$\varepsilon $$ ε -close upper bound on the maximal reachability probability. The result of our procedure … Show more

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Cited by 9 publications
(4 citation statements)
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“…To the best of our knowledge, this was not considered for pBNs before. Future work include finding optimal parameter settings [44], exploiting monotonicity checking [43] and to extend the current work to (parametric) dynamic, Gaussian [12], and recursive BNs [30].…”
Section: Discussionmentioning
confidence: 99%
“…To the best of our knowledge, this was not considered for pBNs before. Future work include finding optimal parameter settings [44], exploiting monotonicity checking [43] and to extend the current work to (parametric) dynamic, Gaussian [12], and recursive BNs [30].…”
Section: Discussionmentioning
confidence: 99%
“…However, for models where most time is spent on model checking the macro-level MDP, the approach is less suitable. We furthermore conjecture that tailored algorithms may exploit some of these dimensions, e.g., when there is the macro-MDP or the subMDPs are indeed MCs or perhaps acyclic, depending on the number of parameters and their influence [36], or based on the relative weight of the uncertain rewards compared to rewards in the macro-MDP.…”
Section: Methodsmentioning
confidence: 99%
“…We denote this region also with [[u − , u + ]]. For regions, we may compute a lower bound on min u∈R ER max M[u] (♦T ) and an upper bound on max u∈R ER max M[u] (♦T ) via parameter lifting [33,36].…”
Section: Regions and Parametric Model Checking A Set Of Valuations De...mentioning
confidence: 99%
“…Recently, [78] intertwined the region verification method outlined in Sect. 5.2 with establishing monotonicity (within that region).…”
Section: Epiloguementioning
confidence: 99%