Soft Computing

, Volume 22, Issue 4, pp 1035–1046 | Cite as

Characterizations of recognizable weighted tree languages by logic and bimorphisms

  • Zoltán FülöpEmail author
  • Heiko Vogler


We give a general definition of weighted tree automata (wta) and define three instances which differ in the underlying weight algebras: semirings, multi-operator monoids, and tree-valuation monoids. Also, we define a general concept of weighted expressions based on monadic second-order logics. In the same way as for wta, we define three instances corresponding to the above-mentioned weight algebras. We prove that wta over semirings are equivalent to weighted expressions over semirings, and prove the same equivalence over tree-valuation monoids. For wta over semirings and for wta over tree-valuation monoids we prove characterizations in terms of bimorphisms.



The authors would like to thank the reviewers for pointing out (small) mistakes and for helpful suggestions.


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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of SzegedSzegedHungary
  2. 2.Faculty of Computer ScienceTechnische Universität DresdenDresdenGermany

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