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C-Maximal Strong Partial Clones and the Inclusion Structure of Boolean Weak Bases
Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, Faculty of Science & Engineering.
2022 (English)In: Journal of Multiple-Valued Logic and Soft Computing, ISSN 1542-3980, E-ISSN 1542-3999, Vol. 38, no 3-4, p. 333-353Article in journal (Refereed) Published
Abstract [en]

Strong partial clones are composition closed sets of partial operations containing all partial projections, characterizable as partial polymorphisms of sets of relations Γ (pPol(Γ)). If C is a clone it is known that the set of all strong partial clones whose total component equals C, has a greatest element pPol(Γω), where Γω is called a weak base. Weak bases have seen applications in computer science due to their usefulness for proving complexity classifications for constraint satisfaction related problems. In this article we (1) completely describe the inclusion structure between pPol(Γω), pPol(Δω) for all Boolean weak bases Γω and Δω and (2) in many such cases prove that the strong partial clones in question uniquely cover each other.

Place, publisher, year, edition, pages
Philadelphia, PA, United States: Old City Publishing, 2022. Vol. 38, no 3-4, p. 333-353
Keywords [en]
Universal algebra, clone theory, partial clone theory, weak bases
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:liu:diva-182644ISI: 000745038100004OAI: oai:DiVA.org:liu-182644DiVA, id: diva2:1634637
Available from: 2022-02-03 Created: 2022-02-03 Last updated: 2022-02-10Bibliographically approved

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Lagerkvist, VictorRoy, Biman

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