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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)

Abstract

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.

Keywords

Power Series Classical Case Formal Power Series Finite Index Minimization Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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