Myhill-Nerode Theorem for Sequential Transducers over Unique GCD-Monoids

  • Andreas Maletti
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3317)


We generalize the classical Myhill-Nerode theorem for finite automata to the setting of sequential transducers over unique GCD-monoids, which are cancellative monoids in which every two non-zero elements admit a unique greatest common (left) divisor. We prove that a given formal power series is sequential, if and only if it is directed and our Myhill-Nerode equivalence relation has finite index. As in the classical case, our Myhill-Nerode equivalence relation also admits the construction of a minimal (with respect to the number of states) sequential transducer recognizing the given formal power series.


Power Series Classical Case Formal Power Series Finite Index Minimization Algorithm 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Andreas Maletti
    • 1
  1. 1.Faculty of Computer ScienceDresden University of TechnologyDresdenGermany

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