Theory of Computing Systems

, Volume 44, Issue 3, pp 455–499 | Cite as

A Kleene Theorem for Weighted Tree Automata over Distributive Multioperator Monoids



Kleene’s theorem on the equivalence of recognizability and rationality for formal tree series over distributive multioperator monoids is proved. As a consequence of this, Kleene’s theorem for weighted tree automata over arbitrary, i.e., not necessarily commutative, semirings is derived.


Recognizable tree series Rational tree series Semirings Multioperator monoids 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Zoltán Fülöp
    • 1
  • Andreas Maletti
    • 2
  • Heiko Vogler
    • 2
  1. 1.Department of Computer ScienceUniversity of SzegedSzegedHungary
  2. 2.Faculty of Computer ScienceDresden University of TechnologyDresdenGermany

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