Codensity Games for Bisimilarity View Full Text


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Article Info

DATE

2022-07

AUTHORS

Yuichi Komorida, Shin-ya Katsumata, Nick Hu, Bartek Klin, Samuel Humeau, Clovis Eberhart, Ichiro Hasuo

ABSTRACT

Bisimilarity as an equivalence notion of systems has been central to process theory. Due to the recent rise of interest in quantitative systems (probabilistic, weighted, hybrid, etc.), bisimilarity has been extended in various ways, such as bisimulation metric between probabilistic systems. An important feature of bisimilarity is its game-theoretic characterization, where Spoiler and Duplicator play against each other; extension of bisimilarity games to quantitative settings has been actively pursued too. In this paper, we present a general framework that uniformly describes game characterizations of bisimilarity-like notions. Our framework is formalized categorically using fibrations and coalgebras. In particular, our characterization of bisimilarity in terms of fibrational predicate transformers allows us to derive what we call codensity bisimilarity games: a general categorical game characterization of bisimilarity. Our framework covers known bisimilarity-like notions (such as bisimulation metric and bisimulation seminorm) as well as new ones (including what we call bisimulation topology). More... »

PAGES

403-465

References to SciGraph publications

  • 2005. The Least Fibred Lifting and the Expressivity of Coalgebraic Modal Logic in ALGEBRA AND COALGEBRA IN COMPUTER SCIENCE
  • 2018-09-20. Fibrational Bisimulations and Quantitative Reasoning in COALGEBRAIC METHODS IN COMPUTER SCIENCE
  • 2009. Weighted Bisimulation in Linear Algebraic Form in CONCUR 2009 - CONCURRENCY THEORY
  • 2019-04-05. Path Category for Free in FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATION STRUCTURES
  • 1981. Concurrency and automata on infinite sequences in THEORETICAL COMPUTER SCIENCE
  • 2007. A Course in Functional Analysis in NONE
  • 2003-02-28. An Intrinsic Characterization of Approximate Probabilistic Bisimilarity in FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATION STRUCTURES
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    http://scigraph.springernature.com/pub.10.1007/s00354-022-00186-y

    DOI

    http://dx.doi.org/10.1007/s00354-022-00186-y

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1149964347


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