Abstract
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.
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The authors would like to thank the reviewers for pointing out (small) mistakes and for helpful suggestions.
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Communicated by M. Droste, Z. Esik and K. Larsen.
The work of the first author was partially supported by the Hungarian Scientific Research Fund (OTKA) under Grant K 108448.
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Fülöp, Z., Vogler, H. Characterizations of recognizable weighted tree languages by logic and bimorphisms. Soft Comput 22, 1035–1046 (2018). https://doi.org/10.1007/s00500-015-1717-2
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DOI: https://doi.org/10.1007/s00500-015-1717-2