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DOI: 10.4230/LIPIcs.CONCUR.2018.17
URN: urn:nbn:de:0030-drops-95552
URL: http://drops.dagstuhl.de/opus/volltexte/2018/9555/
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Bonchi, Filippo ; König, Barbara ; Petrisan, Daniela

Up-To Techniques for Behavioural Metrics via Fibrations

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Abstract

Up-to techniques are a well-known method for enhancing coinductive proofs of behavioural equivalences. We introduce up-to techniques for behavioural metrics between systems modelled as coalgebras and we provide abstract results to prove their soundness in a compositional way. In order to obtain a general framework, we need a systematic way to lift functors: we show that the Wasserstein lifting of a functor, introduced in a previous work, corresponds to a change of base in a fibrational sense. This observation enables us to reuse existing results about soundness of up-to techniques in a fibrational setting. We focus on the fibrations of predicates and relations valued in a quantale, for which pseudo-metric spaces are an example. To illustrate our approach we provide an example on distances between regular languages.

BibTeX - Entry

@InProceedings{bonchi_et_al:LIPIcs:2018:9555,
  author =	{Filippo Bonchi and Barbara K{\"o}nig and Daniela Petrisan},
  title =	{{Up-To Techniques for Behavioural Metrics via Fibrations}},
  booktitle =	{29th International Conference on Concurrency Theory  (CONCUR 2018)},
  pages =	{17:1--17:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-087-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{118},
  editor =	{Sven Schewe and Lijun Zhang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9555},
  URN =		{urn:nbn:de:0030-drops-95552},
  doi =		{10.4230/LIPIcs.CONCUR.2018.17},
  annote =	{Keywords: behavioural metrics, bisimilarity, up-to techniques, coalgebras, fibrations}
}

Keywords: behavioural metrics, bisimilarity, up-to techniques, coalgebras, fibrations
Seminar: 29th International Conference on Concurrency Theory (CONCUR 2018)
Issue Date: 2018
Date of publication: 13.08.2018


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