A Coalgebraic Perspective on Minimization and Determinization

  • Jiří Adámek
  • Filippo Bonchi
  • Mathias Hülsbusch
  • Barbara König
  • Stefan Milius
  • Alexandra Silva
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7213)


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.


Transition System Label Transition System Unique Morphism Input Alphabet Concrete Category 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jiří Adámek
    • 1
  • Filippo Bonchi
    • 2
  • Mathias Hülsbusch
    • 3
  • Barbara König
    • 3
  • Stefan Milius
    • 1
  • Alexandra Silva
    • 4
  1. 1.Technische Universität BraunschweigGermany
  2. 2.CNRS, ENS Lyon, Université de Lyon LIP (UMR 5668)France
  3. 3.Universität Duisburg-EssenGermany
  4. 4.Radboud UniversityNijmegenNetherlands

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