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Adaptive and Sequential Gridding Procedures for the Abstraction and the Verification of Stochastic Processes

Lookup NU author(s): Dr Sadegh Soudjani

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This is the authors' accepted manuscript of an article that has been published in its final definitive form by Society for Industrial and Applied Mathematics, 2013.

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Abstract

This work is concerned with the generation of finite abstractions of general state-space processes, to be employed in the formal verification of probabilistic properties by means of automatic techniques such as probabilistic model checkers. The contribution employs an abstraction procedure based on the partitioning of the state space, which generates a Markov chain as an approximation of the original process. The work puts forward a novel adaptive and sequential gridding algorithm that is expected to conform to the underlying dynamics of the model and thus to mitigate the curse of dimensionality unavoidably related to the partitioning procedure. The results are also extended to the general modeling framework known as Stochastic Hybrid Systems. While the technique is applicable to a wide arena of probabilistic properties, with focus on the study of a particular specification (probabilistic safety or invariance, over a finite horizon) the proposed adaptive algorithm is first benchmarked against a uniform gridding approach taken from the literature, and finally tested on an applicative case study in Biology.


Publication metadata

Author(s): Esmaeil Zadeh Soudjani S, Abate A

Publication type: Article

Publication status: Published

Journal: SIAM Journal on Applied Dynamical Systems

Year: 2013

Volume: 12

Issue: 2

Pages: 921-956

Online publication date: 22/03/2013

Date deposited: 08/11/2019

ISSN (electronic): 1536-0040

Publisher: Society for Industrial and Applied Mathematics

URL: https://doi.org/10.1137/120871456

DOI: 10.1137/120871456


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