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DOI: 10.4230/LIPIcs.FSCD.2020.10

Conditional Bisimilarity for Reactive Systems

Authors: Mathias Hülsbusch, Barbara König, Sebastian Küpper, and Lara Stoltenow

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)

Abstract

Reactive systems à la Leifer and Milner, an abstract categorical framework for rewriting, provide a suitable framework for deriving bisimulation congruences. This is done by synthesizing interactions with the environment in order to obtain a compositional semantics. We enrich the notion of reactive systems by conditions on two levels: first, as in earlier work, we consider rules enriched with application conditions and second, we investigate the notion of conditional bisimilarity. Conditional bisimilarity allows us to say that two system states are bisimilar provided that the environment satisfies a given condition. We present several equivalent definitions of conditional bisimilarity, including one that is useful for concrete proofs and that employs an up-to-context technique, and we compare with related behavioural equivalences. We instantiate reactive systems in order to obtain DPO graph rewriting and consider a case study in this setting.

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Mathias Hülsbusch, Barbara König, Sebastian Küpper, and Lara Stoltenow. Conditional Bisimilarity for Reactive Systems. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{hulsbusch_et_al:LIPIcs.FSCD.2020.10,
  author =	{H\"{u}lsbusch, Mathias and K\"{o}nig, Barbara and K\"{u}pper, Sebastian and Stoltenow, Lara},
  title =	{{Conditional Bisimilarity for Reactive Systems}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{10:1--10:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.10},
  URN =		{urn:nbn:de:0030-drops-123322},
  doi =		{10.4230/LIPIcs.FSCD.2020.10},
  annote =	{Keywords: conditional bisimilarity, reactive systems, up-to context, graph transformation}
}

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DOI: 10.4230/LIPIcs.CALCO.2017.6

On Path-Based Coalgebras and Weak Notions of Bisimulation

Authors: Harsh Beohar and Sebastian Küpper

Published in: LIPIcs, Volume 72, 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)

Abstract

It is well known that the theory of coalgebras provides an abstract definition of behavioural equivalence that coincides with strong bisimulation across a wide variety of state-based systems. Unfortunately, the theory in the presence of so-called silent actions is not yet fully developed. In this paper, we give a coalgebraic characterisation of branching (delay) bisimulation in the context of labelled transition systems (fully probabilistic systems). It is shown that recording executions (up to a notion of stuttering), rather than the set of successor states, from a state is sufficient to characterise the respected bisimulation relations in both cases.

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Harsh Beohar and Sebastian Küpper. On Path-Based Coalgebras and Weak Notions of Bisimulation. In 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 72, pp. 6:1-6:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{beohar_et_al:LIPIcs.CALCO.2017.6,
  author =	{Beohar, Harsh and K\"{u}pper, Sebastian},
  title =	{{On Path-Based Coalgebras and Weak Notions of Bisimulation}},
  booktitle =	{7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)},
  pages =	{6:1--6:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-033-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{72},
  editor =	{Bonchi, Filippo and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2017.6},
  URN =		{urn:nbn:de:0030-drops-80362},
  doi =		{10.4230/LIPIcs.CALCO.2017.6},
  annote =	{Keywords: Paths, Executions, Branching bisimulation, Coalgebras}
}

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Documents authored by Küpper, Sebastian

Conditional Bisimilarity for Reactive Systems

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On Path-Based Coalgebras and Weak Notions of Bisimulation

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