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.MFCS.2023.87
URN: urn:nbn:de:0030-drops-186210
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18621/
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Vialard, Isa

Ordinal Measures of the Set of Finite Multisets

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LIPIcs-MFCS-2023-87.pdf (0.8 MB)

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.

BibTeX - Entry

@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/opus/volltexte/2023/18621},
  URN =		{urn:nbn:de:0030-drops-186210},
  doi =		{10.4230/LIPIcs.MFCS.2023.87},
  annote =	{Keywords: Well-partial order, finite multisets, termination, program verification}
}

Keywords: Well-partial order, finite multisets, termination, program verification
Collection: 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)
Issue Date: 2023
Date of publication: 21.08.2023

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