License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CALCO.2023.12
URN: urn:nbn:de:0030-drops-188094
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Rot, Jurriaan ; WiƟmann, Thorsten

Bisimilar States in Uncertain Structures

LIPIcs-CALCO-2023-12.pdf (0.7 MB)


We provide a categorical notion called uncertain bisimilarity, which allows to reason about bisimilarity in combination with a lack of knowledge about the involved systems. Such uncertainty arises naturally in automata learning algorithms, where one investigates whether two observed behaviours come from the same internal state of a black-box system that can not be transparently inspected. We model this uncertainty as a set functor equipped with a partial order which describes possible future developments of the learning game. On such a functor, we provide a lifting-based definition of uncertain bisimilarity and verify basic properties. Beside its applications to Mealy machines, a natural model for automata learning, our framework also instantiates to an existing compatibility relation on suspension automata, which are used in model-based testing. We show that uncertain bisimilarity is a necessary but not sufficient condition for two states being implementable by the same state in the black-box system. We remedy the lack of sufficiency by a characterization of uncertain bisimilarity in terms of coalgebraic simulations.

BibTeX - Entry

  author =	{Rot, Jurriaan and Wi{\ss}mann, Thorsten},
  title =	{{Bisimilar States in Uncertain Structures}},
  booktitle =	{10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-287-7},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{270},
  editor =	{Baldan, Paolo and de Paiva, Valeria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-188094},
  doi =		{10.4230/LIPIcs.CALCO.2023.12},
  annote =	{Keywords: Coalgebra, Relation Lifting, Bisimilarity, Mealy Machines, ioco}

Keywords: Coalgebra, Relation Lifting, Bisimilarity, Mealy Machines, ioco
Collection: 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)
Issue Date: 2023
Date of publication: 02.09.2023

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