All minimal clones generated by {0,1}-valued majority operations on a five-element set

Behrisch, Mike; Vargas-García, Edith; Wachtel, Andreas

doi:10.1109/ISMVL64713.2025.00042

Record link:

http://hdl.handle.net/20.500.12708/217033

Title:

All minimal clones generated by {0,1}-valued majority operations on a five-element set

Citation:

Behrisch, M., Vargas-García, E., & Wachtel, A. (2025). All minimal clones generated by {0,1}-valued majority operations on a five-element set. In 2025 IEEE 55th International Symposium on Multiple-Valued Logic (ISMVL) (pp. 184–189). IEEE Xplore. https://doi.org/10.1109/ISMVL64713.2025.00042

Publisher DOI:

10.1109/ISMVL64713.2025.00042

Publication Type:

Inproceedings - Full-Paper Contribution

Language:

English

Authors:

Behrisch, Mike
Vargas-García, Edith
Wachtel, Andreas

Organisational Unit:

E104-01 - Forschungsbereich Algebra

Published in:

2025 IEEE 55th International Symposium on Multiple-Valued Logic (ISMVL)

ISBN:

979-8-3315-0745-9

DOI of the book:

10.1109/ISMVL64713.2025

Date (published):

18-Jun-2025

Event name:

2025 IEEE 55th International Symposium on Multiple-Valued Logic (ISMVL)

Event date:

5-Jun-2025 - 6-Jun-2025

Event place:

Montréal, Québec, Canada

Number of Pages:

Publisher:

IEEE Xplore

Peer reviewed:

Yes

Keywords:

minimal clone; cyclically symmetric majority operation; {0,1}-valued majority operation; parallel computing

Abstract:

Based on a computer search we identify all majority operations on {0, 1, 2, 3, 4} with values in {0, 1} on the injective triples that generate a minimal clone. We classify these functions up to an equivalence extending conjugacy (isomorphism) and count the number of majority operations in the generated clones.

Project title:

Orthogonalität und Symmetrie: PIN5424624 (FWF - Österr. Wissenschaftsfonds)

Link (external):

https://doi.org/10.5281/zenodo.13862887
https://doi.org/10.5281/zenodo.13786499

Research Areas:

Computer Science Foundations: 10%
Fundamental Mathematics Research: 90%

Science Branch:

1020 - Informatik: 10%
1010 - Mathematik: 90%

Appears in Collections:

Conference Paper

Show full item record