Coalgebra Encoding for Efficient Minimization

Authors Hans-Peter Deifel , Stefan Milius , Thorsten Wißmann

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Author Details

Hans-Peter Deifel
  • Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
Stefan Milius
  • Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
Thorsten Wißmann
  • Radboud University Nijmegen, The Netherlands


We would like to thank the anonymous referees for their comments, which helped us to improve the presentation.

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Hans-Peter Deifel, Stefan Milius, and Thorsten Wißmann. Coalgebra Encoding for Efficient Minimization. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 28:1-28:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Recently, we have developed an efficient generic partition refinement algorithm, which computes behavioural equivalence on a state-based system given as an encoded coalgebra, and implemented it in the tool CoPaR. Here we extend this to a fully fledged minimization algorithm and tool by integrating two new aspects: (1) the computation of the transition structure on the minimized state set, and (2) the computation of the reachable part of the given system. In our generic coalgebraic setting these two aspects turn out to be surprisingly non-trivial requiring us to extend the previous theory. In particular, we identify a sufficient condition on encodings of coalgebras, and we show how to augment the existing interface, which encapsulates computations that are specific for the coalgebraic type functor, to make the above extensions possible. Both extensions have linear run time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • Theory of computation → Logic and verification
  • Coalgebra
  • Partition refinement
  • Transition systems
  • Minimization


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