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DOI: 10.4230/LIPIcs.CONCUR.2018.37

(Metric) Bisimulation Games and Real-Valued Modal Logics for Coalgebras

Authors: Barbara König and Christina Mika-Michalski

Published in: LIPIcs, Volume 118, 29th International Conference on Concurrency Theory (CONCUR 2018)

Abstract

Behavioural equivalences can be characterized via bisimulations, modal logics and spoiler-defender games. In this paper we review these three perspectives in a coalgebraic setting, which allows us to generalize from the particular branching type of a transition system. We are interested in qualitative notions (classical bisimulation) as well as quantitative notions (bisimulation metrics). Our first contribution is to introduce a spoiler-defender bisimulation game for coalgebras in the classical case. Second, we introduce such games for the metric case and furthermore define a real-valued modal coalgebraic logic, from which we can derive the strategy of the spoiler. For this logic we show a quantitative version of the Hennessy-Milner theorem.

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Barbara König and Christina Mika-Michalski. (Metric) Bisimulation Games and Real-Valued Modal Logics for Coalgebras. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 37:1-37:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{konig_et_al:LIPIcs.CONCUR.2018.37,
  author =	{K\"{o}nig, Barbara and Mika-Michalski, Christina},
  title =	{{(Metric) Bisimulation Games and Real-Valued Modal Logics for Coalgebras}},
  booktitle =	{29th International Conference on Concurrency Theory (CONCUR 2018)},
  pages =	{37:1--37:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-087-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{118},
  editor =	{Schewe, Sven and Zhang, Lijun},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2018.37},
  URN =		{urn:nbn:de:0030-drops-95757},
  doi =		{10.4230/LIPIcs.CONCUR.2018.37},
  annote =	{Keywords: coalgebra, bisimulation games, spoiler-defender games, behavioural metrics, modal logic}
}

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(Metric) Bisimulation Games and Real-Valued Modal Logics for Coalgebras

Abstract

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