Soft Computing

, Volume 22, Issue 4, pp 1103–1120 | Cite as

A generalized partition refinement algorithm, instantiated to language equivalence checking for weighted automata

  • Barbara König
  • Sebastian KüpperEmail author


We present a generic algorithm, generalizing partition refinement, for deciding behavioural equivalences for various types of transition systems. In order to achieve this generality, we work with coalgebra, which offers a general framework for modelling different types of state-based systems. The underlying idea of the algorithm is to work on the so-called final chain and to factor out redundant information. If the algorithm terminates, the result of the construction is a representative of the given coalgebra that is not necessarily unique and that allows to precisely answer questions about behavioural equivalence. We instantiate the algorithm to the particularly interesting case of weighted automata over semirings in order to obtain a procedure for checking language equivalence for a large number of semirings. We use fuzzy automata with weights from an l-monoid as a case study.



We would like to thank Alexandra Silva, Filippo Bonchi, Jacques Sakarovitch and Marcello Bonsangue for several interesting discussions on this topic. Furthermore, we are very grateful to Manfred Droste, Zoltán Ésik and the anonymous reviewers for their helpful comments on this paper. In addition, we would like to thank Christina Mika for her work on the implementation.

Compliance with ethical standards

Conflicts of interest

The authors confirm that there are no known conflicts of interest associated with this publication.


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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Universität Duisburg-EssenDuisburgGermany

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