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Bisimilar States in Uncertain Structures

Authors Jurriaan Rot , Thorsten Wißmann

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  • 17 pages

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Jurriaan Rot
  • Radboud University, Nijmegen, The Netherlands
Thorsten Wißmann
  • Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
  • Radboud University, Nijmegen, The Netherlands

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Jurriaan Rot and Thorsten Wißmann. Bisimilar States in Uncertain Structures. In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 12:1-12:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation
  • Coalgebra
  • Relation Lifting
  • Bisimilarity
  • Mealy Machines
  • ioco


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