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

📝 Original Info

• Title: Characterization of deterministically recognizable weighted tree languages over commutative semifields by finitely generated and cancellative scalar algebras
• ArXiv ID: 2509.14914
• Date: 2025-09-18
• Authors: ** 논문에 명시된 저자 정보가 제공되지 않았습니다. (필요 시 원문을 확인하시기 바랍니다.) **

📝 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.

💡 Deep Analysis

📄 Full Content

Reference