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arXiv · 2509.14914

Characterization of deterministically recognizable weighted tree languages over commutative semifields by finitely generated and cancellative scalar algebras

Zoltán Fülöp·Heiko Vogler
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Abstract

Due to the works of S. Bozapalidis and A. Alexandrakis, there is a well-known characterization of recognizable weighted tree languages over fields in terms of finite-dimensionality of syntactic vector spaces. Here we prove a characterization of bottom-up deterministically recognizable weighted tree languages over commutative semifields in terms of the requirement that the respective m-syntactic scalar algebras are finitely generated. The concept of scalar algebra is introduced in this paper; it is obtained from the concept of vector space by disregarding the addition of vectors. Moreover, we prove a minimization theorem for bottom-up-deterministic weighted tree automata and we construct the minimal automaton.

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Zoltán Fülöp, Heiko Vogler. 2025-09-18. Characterization of deterministically recognizable weighted tree languages over commutative semifields by finitely generated and cancellative scalar algebras. https://arxiv.org/abs/2509.14914

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