Abstract
The critical relations are the building blocks of the relational clone of a relational structure with respect to the relational operations intersection and direct product. In this paper we describe the critical relations of crowns. As a consequence, we obtain that the subpower membership problem for any crown is polynomial-time solvable.
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References
Baker, K., Pixley, F.F.: Polynomial interpolation and the Chinese Remainder Theorem for algebraic systems. Math. Z. 143, 165–174 (1975)
Bulatov, A., Mayr, P., Szendrei, Á.: The subpower membership problem for finite algebras with cube terms. Logical Methods in Computer Science 15/1, 11:1–11:48 (2019)
Demetrovics, J., Rónyai, L.: Algebraic properties of crowns and fences. Order 6(/1), 91–99 (1989)
Geiger, D.: Closed systems of functions and predicates. Pacific J. Math. 27, 95–100 (1968)
Jablonskiy, S.V.: On functional completeness in the three-valued calculus (Russian). Dokl. Akad. Nauk. SSSR 95, 1153–1155 (1954)
Kearnes, K., Szendrei, Á.: Clones of algebras with parallelogram terms. Internat. J. Algebra Comput. 22/1, 1250005 30 (2012)
Larose, B., Zádori, L.: The complexity of the extendibility problem for finite posets. SIAM J. Discret. Math. 17(/1), 114–121 (2003)
McKenzie, R.: Monotone clones, residual smallness and congruence distributivity. Bull. Austral. Math. Soc. 41, 283–300 (1990)
Pratt, V., Tiuryn, J.: Satisfiability of inequalities in a poset. Fund Inform. 28, 165–182 (1996)
Tardos, G.: A maximal clone of monotone operations which is not finitely generated. Order 3/3, 211–218 (1986)
Willard, R.: Four Unsolved Problems in Congruence Permutable Varieties. Talk at the “Conference on Order, Algebra, and Logics”, Nashville (2007)
Zádori, L.: Posets, near unanimity functions and zigzags. Bull. Aust. Math. Soc. 47(/1), 79–93 (1993)
Zádori, L.: Series-parallel posets with non-finitely generated clones. Order 10/4, 305–316 (1993)
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The research of authors was supported by the grants TUDFO/47138-1/2019-ITM and NKFIH-1279-2/2020 of the Ministry for Innovation and Technology, Hungary, the EU-funded Hungarian grant EFOP-3.6.2-16-2017-00015, and the NKFIH grants K115518 and K128042. The third author was also supported by the Alfréd Rényi Institute of Mathematics, ELKH, Hungary.
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Kunos, Á., Maróti, M. & Zádori, L. Critical Relations of Crowns in Critical Times of Coronavirus Depression. Order 39, 229–241 (2022). https://doi.org/10.1007/s11083-021-09571-6
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DOI: https://doi.org/10.1007/s11083-021-09571-6