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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.FSTTCS.2011.191

Conditional Reactive Systems

Authors: H. J. Sander Bruggink, Raphaël Cauderlier, Mathias Hülsbusch, and Barbara König

Published in: LIPIcs, Volume 13, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)

Abstract

We lift the notion of nested application conditions from graph transformation systems to the general categorical setting of reactive systems as defined by Leifer and Milner. This serves two purposes: first, we enrich the formalism of reactive systems by adding application conditions for rules; second, it turns out that some constructions for graph transformation systems (such as computing weakest preconditions and strongest postconditions and showing local confluence by means of critical pair analysis) can be done very elegantly in the more general setting.

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H. J. Sander Bruggink, Raphaël Cauderlier, Mathias Hülsbusch, and Barbara König. Conditional Reactive Systems. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 13, pp. 191-203, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{bruggink_et_al:LIPIcs.FSTTCS.2011.191,
  author =	{Bruggink, H. J. Sander and Cauderlier, Rapha\"{e}l and H\"{u}lsbusch, Mathias and K\"{o}nig, Barbara},
  title =	{{Conditional Reactive Systems}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)},
  pages =	{191--203},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-34-7},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{13},
  editor =	{Chakraborty, Supratik and Kumar, Amit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2011.191},
  URN =		{urn:nbn:de:0030-drops-33257},
  doi =		{10.4230/LIPIcs.FSTTCS.2011.191},
  annote =	{Keywords: reactive systems, graph transformation, graph logic, Hoare triples, critical pair analysis}
}

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Conditional Bisimilarity for Reactive Systems

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Conditional Reactive Systems

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