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Bisimilarity of Diagrams

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Relational and Algebraic Methods in Computer Science (RAMiCS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12062))

Abstract

In this paper, we investigate diagrams, namely functors from any small category to a fixed category, and more particularly, their bisimilarity. Initially defined using the theory of open maps of Joyal et al., we prove two characterisations of this bisimilarity: it is equivalent to the existence of a bisimulation-like relation and has a logical characterisation à la Hennessy and Milner. We then prove that we capture both path bisimilarity and strong path bisimilarity of any small open maps situation. We then look at the particular case of finitary diagrams with values in real or rational vector spaces. We prove that checking bisimilarity and satisfiability of a positive formula by a diagram are both decidable by reducing to a problem of existence of invertible matrices with linear conditions, which in turn reduces to the existential theory of the reals.

The author was supported by ERATO HASUO Metamathematics for Systems Design Project (No. JPMJER1603), JST and Grant-in-aid No. 19K20215, JSPS.

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Authors and Affiliations

  1. National Institute of Informatics, Tokyo, Japan

    Jérémy Dubut

  2. Japanese-French Laboratory of Informatics, CNRS IRL 3527, Tokyo, Japan

    Jérémy Dubut

Authors
  1. Jérémy Dubut
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Correspondence to Jérémy Dubut .

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Editors and Affiliations

  1. Laboratoire d’informatique (LIX), École Polytechnique, Palaiseau, France

    Uli Fahrenberg

  2. Faculty of Mathematics, Chapman University, Orange, CA, USA

    Peter Jipsen

  3. Department of Computer Science, Brock University, St. Catharines, ON, Canada

    Michael Winter

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Dubut, J. (2020). Bisimilarity of Diagrams. In: Fahrenberg, U., Jipsen, P., Winter, M. (eds) Relational and Algebraic Methods in Computer Science. RAMiCS 2020. Lecture Notes in Computer Science(), vol 12062. Springer, Cham. https://doi.org/10.1007/978-3-030-43520-2_5

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  • DOI: https://doi.org/10.1007/978-3-030-43520-2_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-43519-6

  • Online ISBN: 978-3-030-43520-2

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