2026-07-26T17:25:52Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:18621 2024-03-06T11:02:17Z ddc:004 open_access

Ordinal Measures of the Set of Finite Multisets Vialard, Isa Well-partial order finite multisets termination program verification 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Isa Vialard 2023 Is Part Of LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2023.87 urn:nbn:de:0030-drops-186210 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.87 eng https://creativecommons.org/licenses/by/4.0/legalcode