License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2022.6
URN: urn:nbn:de:0030-drops-157266
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Baudru, Nicolas ; Dando, Louis-Marie ; Lhote, Nathan ; Monmege, Benjamin ; Reynier, Pierre-Alain ; Talbot, Jean-Marc

Weighted Automata and Expressions over Pre-Rational Monoids

LIPIcs-CSL-2022-6.pdf (0.7 MB)


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.

BibTeX - Entry

  author =	{Baudru, Nicolas and Dando, Louis-Marie and Lhote, Nathan and Monmege, Benjamin and Reynier, Pierre-Alain and Talbot, Jean-Marc},
  title =	{{Weighted Automata and Expressions over Pre-Rational Monoids}},
  booktitle =	{30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-218-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{216},
  editor =	{Manea, Florin and Simpson, Alex},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-157266},
  doi =		{10.4230/LIPIcs.CSL.2022.6},
  annote =	{Keywords: Weighted Automata and Expressions, Inverse Monoids, Two-Way Automata}

Keywords: Weighted Automata and Expressions, Inverse Monoids, Two-Way Automata
Collection: 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)
Issue Date: 2022
Date of publication: 27.01.2022

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