Abstract
AbstractParametric 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 actually provides an almost-optimal parameter valuation along with this upper bound.We propose to tackle these ETR-hard problems by a tight combination of two significantly different techniques: monotonicity checking and parameter lifting. The former builds a partial order on states to check whether a pMC is (local or global) monotonic in a certain parameter, whereas parameter lifting is an abstraction technique based on the iterative evaluation of pMCs without parameter dependencies. We explain our novel algorithmic approach and experimentally show that we significantly improve the time to determine almost-optimal synthesis.
Publisher
Springer International Publishing
Reference28 articles.
1. Ábrahám, E., Bartocci, E., Bonakdarpour, B., Dobe, O.: Parameter synthesis for probabilistic hyperproperties. In: Proc. of LPAR. EPiC Series in Computing, vol. 73, pp. 12–31. EasyChair (2020)
2. Aflaki, S., Volk, M., Bonakdarpour, B., Katoen, J.P., Storjohann, A.: Automated fine tuning of probabilistic self-stabilizing algorithms. In: SRDS. IEEE CS (2017)
3. Baier, C., de Alfaro, L., Forejt, V., Kwiatkowska, M.: Model checking probabilistic systems. In: Handbook of Model Checking. Springer (2018)
4. Baier, C., Katoen, J.P.: Principles of Model Checking. MIT Press (2008)
5. Ceska, M., Dannenberg, F., Paoletti, N., Kwiatkowska, M., Brim, L.: Precise parameter synthesis for stochastic biochemical systems. Acta Inf. 54(6) (2017)
Cited by
7 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献