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On the Average Complexity of Moore's State Minimization Algorithm

Authors Frederique Bassino, Julien David, Cyril Nicaud

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Frederique Bassino
Julien David
Cyril Nicaud

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Frederique Bassino, Julien David, and Cyril Nicaud. On the Average Complexity of Moore's State Minimization Algorithm. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 123-134, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2009)


We prove that, for any arbitrary finite alphabet and for the uniform distribution over deterministic and accessible automata with $n$ states, the average complexity of Moore's state minimization algorithm is in $\mathcal{O}(n \log n)$. Moreover this bound is tight in the case of unary automata.
  • Finite automata
  • State minimization
  • Moore’s algorithm
  • Average complexity


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