The minimal arity of near unanimity polymorphisms
-
Libor Barto
and
Ondřej Draganov
Abstract
Dmitriy Zhuk has proved that there exist relational structures which admit near unanimity polymorphisms, but the minimum arity of such a polymorphism is large and almost matches the known upper bounds. We present a simplified and explicit construction of such structures and a detailed, self–contained proof.
This work was supported by the Czech Science Foundation Grant No. 13-01832S.
(Communicated by Miroslav Ploščica)
References
[1] Barto, L.: Finitely related algebras in congruence distributive varieties have near unanimity terms, Canad. J. Math. 65(1) (2013), 3–21.10.4153/CJM-2011-087-3Search in Google Scholar
[2] Barto, L.—Bulín, J.: Deciding absorption in relational structures, Algebra Universalis 78(1) (2017), 3–18.10.1007/s00012-017-0440-5Search in Google Scholar
[3] Barto, L.—Kozik, M.: Absorbing subalgebras, cyclic terms, and the constraint satisfaction problem, Log. Methods Comput. Sci. 8(1) (2012).10.2168/LMCS-8(1:7)2012Search in Google Scholar
[4] Barto, L.—Krokhin, A.—Willard, R.: Polymorphisms, and how to use them. In: The Constraint Satisfaction Problem: Complexity and Approximability (A. Krokhin, S. Zivny, eds.), Dagstuhl Follow-Ups 7, Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2017, pp. 1–44.Search in Google Scholar
[5] Bergman, C.: Universal Algebra: Fundamentals and Selected Topics. Pure Appl. Math., Taylor and Francis, 2011.10.1201/9781439851302Search in Google Scholar
[6] Bulín, J.: Decidability of absorption in relational structures of bounded width, Algebra Universalis 72(1) (2014), 15–28.10.1007/s00012-014-0283-2Search in Google Scholar
[7] Burris, S. N.—Sankappanavar, H. P.: A Course in Universal Algebra. Graduate Texts in Math. 78, Springer-Verlag, New York, 1981.10.1007/978-1-4613-8130-3Search in Google Scholar
[8] Feder, T.—Vardi, M. Y.: The computational structure of monotone monadic snp and constraint satisfaction: A study through datalog and group theory, SIAM J. Comput. 28(1) (1998), 57–104.10.1137/S0097539794266766Search in Google Scholar
[9] Larose, B.—Loten, B. C.—Zádori, L.: A polynomial-time algorithm for near-unanimity graphs, J. Algorithms 55 (2005), 177–191.10.1016/j.jalgor.2004.04.011Search in Google Scholar
[10] Maróti, M.: The existence of a near-unanimity term in a finite algebra is decidable, J. Symbolic Logic 74(3) (2009), 1001–1014.10.2178/jsl/1245158096Search in Google Scholar
[11] Maróti, M.—McKenzie, R.: Existence theorems for weakly symmetric operations, Algebra Universalis 59(3-4) (2008), 463–489.10.1007/s00012-008-2122-9Search in Google Scholar
[12] Zhuk, D. N.: The existence of a near-unanimity function is decidable, Algebra Universalis 71(1) (2014), 31–54.10.1007/s00012-013-0259-7Search in Google Scholar
© 2019 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Regular papers
- RNDr. Miloslav Duchoň, DrSc. passed away ∗ aug. 21, 1932 – †dec. 31, 2018
- Prof. RNDr. Gejza Wimmer, DrSc. – A Septuagenerian?
- Two monads on the category of graphs
- Entropy of MV-algebraic dynamical systems: An example
- Going up and lying over in congruence-modular algebras
- The minimal arity of near unanimity polymorphisms
- On the logarithmic derivative of zeta functions for compact even-dimensional locally symmetric spaces of real rank one
- The generalized Fermat Conjecture
- Evaluation of sums involving products of Gaussian q-binomial coefficients with applications
- Integrals of logarithmic functions and alternating multiple zeta values
- An abelian subextension of the dyadic division field of a hyperelliptic Jacobian
- The class of all semigroups related to semihypergroups of order 2
- Criterion for the weak potency of certain HNN extensions
- Fekete Szegö theorem for a close-to-convex error function
- Bounds for distance between eigenvalues of boundary value problems with retarded argument
- Gradient estimates for a nonlinear heat equation under the Finsler-Ricci flow
- Weak module amenability of triangular banach algebras II
- Some consequences of quasicentral approximate units modulo Hilbert-Schmidt class
- Example of C-rigid polytopes which are not B-rigid
- Some comments on rU-spaces
- On the equivalence of various definitions of mixed poisson processes
- A note on discrete C-embedded subspaces
