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Documents authored by Vialard, Isa

Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.171
A Tropical Approach to the Compositional Piecewise Complexity of Words and Compressed Words

Authors: Philippe Schnoebelen, J. Veron, and Isa Vialard

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We express the piecewise complexity of words using tools and concepts from tropical algebra. This allows us to define a notion of piecewise signature of a word that has size log(n)m^{O(1)} where m is the alphabet size and n is the length of the word. The piecewise signature of a concatenation can be computed from the signatures of its components, allowing a polynomial-time algorithm for computing the piecewise complexity of SLP-compressed words.
Cite as

Philippe Schnoebelen, J. Veron, and Isa Vialard. A Tropical Approach to the Compositional Piecewise Complexity of Words and Compressed Words. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 171:1-171:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{schnoebelen_et_al:LIPIcs.ICALP.2025.171,
  author =	{Schnoebelen, Philippe and Veron, J. and Vialard, Isa},
  title =	{{A Tropical Approach to the Compositional Piecewise Complexity of Words and Compressed Words}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{171:1--171:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.171},
  URN =		{urn:nbn:de:0030-drops-235481},
  doi =		{10.4230/LIPIcs.ICALP.2025.171},
  annote =	{Keywords: Tropical semiring, Subwords and subsequences, piecewise complexity, SLP-compressed words}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.87
Ordinal Measures of the Set of Finite Multisets

Authors: Isa Vialard

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
Well-partial orders, and the ordinal invariants used to measure them, are relevant in set theory, program verification, proof theory and many other areas of computer science and mathematics. In this article we focus on a common data structure in programming, finite multisets of some well partial order. There are two natural orders one can define on the set of finite multisets of a partial order: the multiset embedding and the multiset ordering. Though the maximal order type of these orders is already known, other ordinal invariants remain mostly unknown. Our main contributions are expressions to compute compositionally the width of the multiset embedding and the height of the multiset ordering. Furthermore, we provide a new ordinal invariant useful for characterizing the width of the multiset ordering.
Cite as

Isa Vialard. Ordinal Measures of the Set of Finite Multisets. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 87:1-87:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{vialard:LIPIcs.MFCS.2023.87,
  author =	{Vialard, Isa},
  title =	{{Ordinal Measures of the Set of Finite Multisets}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{87:1--87:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.87},
  URN =		{urn:nbn:de:0030-drops-186210},
  doi =		{10.4230/LIPIcs.MFCS.2023.87},
  annote =	{Keywords: Well-partial order, finite multisets, termination, program verification}
}
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