Pushing for weighted tree automata
- A weight normalization procedure, commonly called pushing, is introduced for weighted tree automata (wta) over commutative semifields. The normalization preserves the recognized weighted tree language even for nondeterministic wta, but it is most useful for bottom-up deterministic wta, where it can be used for minimization and equivalence testing. In both applications a careful selection of the weights to be redistributed followed by normalization allows a reduction of the general problem to the corresponding problem for bottom-up deterministic unweighted tree automata. This approach was already successfully used by Mohri and Eisner for the minimization of deterministic weighted string automata. Moreover, the new equivalence test for two wta M and M′ runs in time O((|M|+|M′|)⋅log(|Q|+|Q′|)), where Q and Q′ are the states of M and M′, respectively, which improves the previously best run-time O(|M|⋅|M′|).
Author details: | Thomas Hanneforth, Andreas Maletti, Daniel Quernheim |
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DOI: | https://doi.org/10.23638/LMCS-14(1:5)2018 |
ISSN: | 1860-5974 |
Title of parent work (English): | Logical Methods in Computer Science |
Subtitle (English): | Dedicated to the memory of Zoltan Esik (1951-2016) |
Publisher: | Logical Methods in Computer Science E V |
Place of publishing: | Braunschweig |
Publication type: | Article |
Language: | English |
Date of first publication: | 2018/01/16 |
Publication year: | 2018 |
Release date: | 2022/04/01 |
Tag: | equivalence testing; minimization; pushing weighted tree automaton |
Volume: | 14 |
Issue: | 1 |
Number of pages: | 16 |
Funding institution: | German Research Foundation (DFG)German Research Foundation (DFG) [MA / 4959 / 1-1] |
Organizational units: | Humanwissenschaftliche Fakultät / Strukturbereich Kognitionswissenschaften / Department Linguistik |
DDC classification: | 4 Sprache / 41 Linguistik / 410 Linguistik |