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International Conference on Foundations of Software Science and Computational Structures

FoSSaCS 2012: Foundations of Software Science and Computational Structures pp 58–73Cite as

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A Coalgebraic Perspective on Minimization and Determinization

A Coalgebraic Perspective on Minimization and Determinization

  • Jiří Adámek17,
  • Filippo Bonchi18,
  • Mathias Hülsbusch19,
  • Barbara König19,
  • Stefan Milius17 &
  • …
  • Alexandra Silva20 
  • Conference paper
  • 1011 Accesses

  • 19 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7213)

Abstract

Coalgebra offers a unified theory of state based systems, including infinite streams, labelled transition systems and deterministic automata. In this paper, we use the coalgebraic view on systems to derive, in a uniform way, abstract procedures for checking behavioural equivalence in coalgebras, which perform (a combination of) minimization and determinization. First, we show that for coalgebras in categories equipped with factorization structures, there exists an abstract procedure for equivalence checking. Then, we consider coalgebras in categories without suitable factorization structures: under certain conditions, it is possible to apply the above procedure after transforming coalgebras with reflections. This transformation can be thought of as some kind of determinization. We will apply our theory to the following examples: conditional transition systems and (non-deterministic) automata.

Keywords

  • Transition System
  • Label Transition System
  • Unique Morphism
  • Input Alphabet
  • Concrete Category

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The work of Mathias Hülsbusch and Barbara König was partially supported by the DFG project Bevaviour-GT. The work of Alexandra Silva was partially supported by Fundação para a Ciência e a Tecnologia, Portugal, under grant number SFRH/BPD/71956/2010.

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Author information

Authors and Affiliations

  1. Technische Universität Braunschweig, Germany

    Jiří Adámek & Stefan Milius

  2. CNRS, ENS Lyon, Université de Lyon LIP (UMR 5668), France

    Filippo Bonchi

  3. Universität Duisburg-Essen, Germany

    Mathias Hülsbusch & Barbara König

  4. Radboud University, Nijmegen, Netherlands

    Alexandra Silva

Authors
  1. Jiří Adámek
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  2. Filippo Bonchi
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  3. Mathias Hülsbusch
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  4. Barbara König
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  5. Stefan Milius
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  6. Alexandra Silva
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Editor information

Editors and Affiliations

  1. IT University of Copenhagen, Rued Langgaards Vej 7, 2300, Copenhagen, Denmark

    Lars Birkedal

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Adámek, J., Bonchi, F., Hülsbusch, M., König, B., Milius, S., Silva, A. (2012). A Coalgebraic Perspective on Minimization and Determinization. In: Birkedal, L. (eds) Foundations of Software Science and Computational Structures. FoSSaCS 2012. Lecture Notes in Computer Science, vol 7213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28729-9_4

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  • DOI: https://doi.org/10.1007/978-3-642-28729-9_4

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  • Print ISBN: 978-3-642-28728-2

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