Asymptotic perturbation bounds for probabilistic model checking with empirically determined probability parameters

Su, G. and Feng, Y. and Chen, Taolue and Rosenblum, D.S. (2015) Asymptotic perturbation bounds for probabilistic model checking with empirically determined probability parameters. IEEE Transactions on Software Engineering 42 (7), pp. 623-639. ISSN 0098-5589.

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Official URL: https://doi.org/10.1109/TSE.2015.2508444

Abstract

Probabilistic model checking is a verification technique that has been the focus of intensive research for over a decade. One important issue with probabilistic model checking, which is crucial for its practical significance but is overlooked by the state-of-the-art largely, is the potential discrepancy between a stochastic model and the real-world system it represents when the model is built from statistical data. In the worst case, a tiny but nontrivial change to some model quantities might lead to misleading or even invalid verification results. To address this issue, in this paper, we present a mathematical characterization of the consequences of model perturbations on the verification distance. The formal model that we adopt is a parametric variant of discrete-time Markov chains equipped with a vector norm to measure the perturbation. Our main technical contributions include a closed-form formulation of asymptotic perturbation bounds, and computational methods for two arguably most useful forms of those bounds, namely linear bounds and quadratic bounds. We focus on verification of reachability properties but also address automata-based verification of omega-regular properties. We present the results of a selection of case studies that demonstrate that asymptotic perturbation bounds can accurately estimate maximum variations of verification results induced by model perturbations.

Metadata

Item Type:	Article
School:	Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
Depositing User:	Taolue Chen
Date Deposited:	27 Sep 2017 11:11
Last Modified:	09 Aug 2023 12:42
URI:	https://eprints.bbk.ac.uk/id/eprint/19654

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