Myhill-Nerode Theorem for Recognizable Tree Series Revisited

  • Andreas Maletti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4957)


In this contribution the Myhill-Nerode congruence relation on tree series is reviewed and a more detailed analysis of its properties is presented. It is shown that, if a tree series is deterministically recognizable over a zero-divisor free and commutative semiring, then the Myhill-Nerode congruence relation has finite index. By [Borchardt: Myhill-Nerode Theorem for Recognizable Tree Series. LNCS 2710. Springer 2003] the converse holds for commutative semifields, but not in general. In the second part, a slightly adapted version of the Myhill-Nerode congruence relation is defined and a characterization is obtained for all-accepting weighted tree automata over multiplicatively cancellative and commutative semirings.


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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Andreas Maletti
    • 1
  1. 1.International Computer Science InstituteBerkeleyUSA

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