Abstract
The 93 minions of Boolean functions stable under left composition with the clone of self-dual monotone functions are described. As an easy consequence, all \((C_1,C_2)\)-clonoids of Boolean functions are determined for an arbitrary clone \(C_1\) and for any clone \(C_2\) containing the clone of self-dual monotone functions.
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References
Aichinger, E., Mayr, P.: Finitely generated equational classes. J. Pure Appl. Algebra 220, 2816–2827 (2016)
Barto, L., Bulín, J., Krokhin, A., Opršal, J.: Algebraic approach to promise constraint satisfaction. J. ACM 68(4), 28 (2021)
Bergman, C.: Universal Algebra. Fundamentals and Selected Topics. CRC Press, Boca Raton (2012)
Couceiro, M., Foldes, S.: Functional equations, constraints, definability of function classes, and functions of Boolean variables. Acta Cybernet. 18, 61–75 (2007)
Couceiro, M., Foldes, S.: Function classes and relational constraints stable under compositions with clones. Discuss. Math. Gen. Algebra Appl. 29, 109–121 (2009)
Couceiro, M., Lehtonen, E.: Stability of Boolean function classes with respect to clones of linear functions. Order (2023)
Kreinecker, S.: Closed function sets on groups of prime order. J. Mult. Valued Logic Soft Comput. 33, 51–74 (2019)
Pippenger, N.: Galois theory for minors of finite functions. Disc. Math. 254, 405–419 (2002)
Post, E.L.: The Two-Valued Iterative Systems of Mathematical Logic. Annals of Mathematics Studies, vol. 5. Princeton University Press, Princeton (1941)
Sparks, A.: On the number of clonoids. Algebra Univ. 80(4), 53 (2019)
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The author would like to thank Miguel Couceiro and Sebastian Kreinecker for inspiring discussions and the anonymous reviewer for thoughtful comments and suggestions that helped improve the manuscript.
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Communicated by This work is funded by National Funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the project UIDB/00297/2020 (Center for Mathematics and Applications) and the project PTDC/MAT-PUR/31174/2017.
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Lehtonen, E. Majority-closed minions of Boolean functions. Algebra Univers. 85, 6 (2024). https://doi.org/10.1007/s00012-023-00835-3
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DOI: https://doi.org/10.1007/s00012-023-00835-3