Efficient Coalgebraic Partition Refinement

Authors Ulrich Dorsch, Stefan Milius, Lutz Schröder, Thorsten Wißmann

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Ulrich Dorsch
Stefan Milius
Lutz Schröder
Thorsten Wißmann

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Ulrich Dorsch, Stefan Milius, Lutz Schröder, and Thorsten Wißmann. Efficient Coalgebraic Partition Refinement. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 32:1-32:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in reactive verification; coalgebraic generality implies in particular that we cover not only classical relational systems but also various forms of weighted systems. Under assumptions on the type functor that allow representing its finite coalgebras in terms of nodes and edges, our algorithm runs in time O(m log n) where n and m are the numbers of nodes and edges, respectively. Instances of our generic algorithm thus match the runtime of the best known algorithms for unlabelled transition systems, Markov chains, and deterministic automata (with fixed alphabets), and improve the best known algorithms for Segala systems.
  • markov chains
  • deterministic finite automata
  • partition refinement
  • generic algorithm
  • paige-tarjan algorithm
  • transition systems


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