Abstract
\(\epsilon \)-bisimulation provides a kind of abstraction description for the correctness of software with probabilistic information. \(\epsilon \)-limit bisimulation had been proposed, which entails that specification is the limit of implementations based on \(\epsilon \)-bisimulation. In this paper, we only focus on the topological properties of \(\epsilon \)-limit bisimulation. According to the definition of \(\epsilon \)-limit bisimulation, several closure constructions are established, such as subnet closure, tail closure, natural extension and iteration. These closure constructions are useful to characterize properties of software.
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Acknowledgments
The work is supported by the NSFC grant (61300048), the Anhui Provincial Natural Science Foundation grant (1508085MA14), the Key Natural Science Foundation grant of Universities of Anhui Province (KJ2014A223), the Excellent Young Talents in Universities of Anhui Province, the major teaching reform project of Anhui higher education revitalization plan (2014ZDJY058), the provincial teaching research project of Anhui province (2015JYXM157), the teaching research project of Huaibei Normal Unversity (JY15118) and the excellent teacher project of Huaibei Normal University (2015ZYJS185). The author would like to thank Professor S.A. Smolka for his invaluable suggestions about the topological properties of \(\epsilon \)- limit bisimulation.
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Ma, YF., Chen, L. (2017). Topological Constructions of Epsilon-Bisimulation. In: Fan, TH., Chen, SL., Wang, SM., Li, YM. (eds) Quantitative Logic and Soft Computing 2016. Advances in Intelligent Systems and Computing, vol 510. Springer, Cham. https://doi.org/10.1007/978-3-319-46206-6_22
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DOI: https://doi.org/10.1007/978-3-319-46206-6_22
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