Sound over-approximation of probabilities

Moggi, Eugenio and Taha, Walid and Thunberg, Johan: Sound over-approximation of probabilities. In: Acta cybernetica, (24) 3. pp. 269-285. (2020)

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Abstract

Safety analysis of high confidence systems requires guaranteed bounds on the probabilities of events of interest. Establishing the correctness of algorithms that aim to compute such bounds is challenging. We address this problem in three steps. First, we use monadic transition systems (MTS) in the category of sets as a framework for modeling discrete time systems. MTS can capture different types of system behaviors, but we focus on a combination of non-deterministic and probabilistic behaviors that often arises when modeling complex systems. Second, we use the category of posets and monotonic maps as a setting to define and compare approximations. In particular, for the MTS of interest, we consider approximations of their configurations based on complete lattices. Third, by restricting to finite lattices, we obtain algorithms that compute over-approximations, i.e., bounds from above within some partial order of approximants, of the system configuration after n steps. Interestingly, finite lattices of “interval probabilities” may fail to accurately approximate configurations that are both non-deterministic and probabilistic, even for deterministic (and continuous) system dynamics. However, better choices of finite lattices are available.

Item Type: Article
Heading title: Uncertainty modeling, software verified computing and optimization
Journal or Publication Title: Acta cybernetica
Date: 2020
Volume: 24
Number: 3
ISSN: 0324-721X
Page Range: pp. 269-285
Publisher: University of Szeged, Institute of Informatics
Place of Publication: Szeged
Event Title: Summer Workshop on Interval Methods (11.) (2018) (Rostock)
Related URLs: http://acta.bibl.u-szeged.hu/69263/
DOI: https://doi.org/10.14232/actacyb.24.3.2020.2
Uncontrolled Keywords: Számítástechnika, Kibernetika
Additional Information: Bibliogr.: 285. p. ; összefoglalás angol nyelven
Subjects: 01. Natural sciences
01. Natural sciences > 01.02. Computer and information sciences
Date Deposited: 2020. Jul. 30. 12:49
Last Modified: 2020. Jul. 30. 12:53
URI: http://acta.bibl.u-szeged.hu/id/eprint/69287

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