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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.2023.69
URN: urn:nbn:de:0030-drops-186030
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18603/
Nakamura, Yoshiki
On the Finite Variable-Occurrence Fragment of the Calculus of Relations with Bounded Dot-Dagger Alternation
Abstract
We introduce the k-variable-occurrence fragment, which is the set of terms having at most k occurrences of variables. We give a sufficient condition for the decidability of the equational theory of the k-variable-occurrence fragment using the finiteness of a monoid. As a case study, we prove that for Tarski’s calculus of relations with bounded dot-dagger alternation (an analogy of quantifier alternation in first-order logic), the equational theory of the k-variable-occurrence fragment is decidable for each k.
BibTeX - Entry
@InProceedings{nakamura:LIPIcs.MFCS.2023.69,
author = {Nakamura, Yoshiki},
title = {{On the Finite Variable-Occurrence Fragment of the Calculus of Relations with Bounded Dot-Dagger Alternation}},
booktitle = {48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
pages = {69:1--69:15},
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/2023/18603},
URN = {urn:nbn:de:0030-drops-186030},
doi = {10.4230/LIPIcs.MFCS.2023.69},
annote = {Keywords: Relation algebra, First-order logic, Decidable fragment, Monoid}
}
