2026-07-25T06:06:27Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:15726 2024-03-06T10:56:03Z ddc:004 open_access

Weighted Automata and Expressions over Pre-Rational Monoids Baudru, Nicolas Dando, Louis-Marie Lhote, Nathan Monmege, Benjamin Reynier, Pierre-Alain Talbot, Jean-Marc Weighted Automata and Expressions Inverse Monoids Two-Way Automata The Kleene theorem establishes a fundamental link between automata and expressions over the free monoid. Numerous generalisations of this result exist in the literature; on one hand, lifting this result to a weighted setting has been widely studied. On the other hand, beyond the free monoid, different monoids can be considered: for instance, two-way automata, and even tree-walking automata, can be described by expressions using the free inverse monoid. In the present work, we aim at combining both research directions and consider weighted extensions of automata and expressions over a class of monoids that we call pre-rational, generalising both the free inverse monoid and graded monoids. The presence of idempotent elements in these pre-rational monoids leads in the weighted setting to consider infinite sums. To handle such sums, we will have to restrict ourselves to rationally additive semirings. Our main result is thus a generalisation of the Kleene theorem for pre-rational monoids and rationally additive semirings. As a corollary, we obtain a class of expressions equivalent to weighted two-way automata, as well as one for tree-walking automata. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Nicolas Baudru and Louis-Marie Dando and Nathan Lhote and Benjamin Monmege and Pierre-Alain Reynier and Jean-Marc Talbot 2022 Is Part Of LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2022.6 urn:nbn:de:0030-drops-157266 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.6 eng https://creativecommons.org/licenses/by/4.0/legalcode