Abstract
We prove that whenever \({\mathbb {A}}\) is a 3-conservative relational structure with only binary and unary relations, then the algebra of polymorphisms of \({\mathbb {A}}\) either has no Taylor operation (i.e., CSP(\({\mathbb {A}}\)) is NP-complete), or it generates an SD(\({\wedge}\)) variety (i.e., CSP(\({\mathbb {A}}\)) has bounded width).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Atserias A.: On digraph coloring problems and treewidth duality. European J. Combin. 29, 796–820 (2008)
Barto, L.: The dichotomy for conservative constraint satisfaction problems revisited. In: 26th Annual IEEE Symposium on Logic in Computer Science (LICS 2011), pp. 301–310. IEEE, Washington (2011)
Barto, L., Kozik, M.: Constraint satisfaction problems of bounded width. In: 50th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2009), pp. 595–603. IEEE, Atlanta (2009)
Bodnarchuk V., Kaluzhnin L., Kotov V., Romov B.: Galois theory for Post algebras. I. Cybernetics 5, 243–252 (1969)
Bulatov, A.A.: Complexity of conservative constraint satisfaction problems. ACM Trans. Comput. Log. 12, 24:1–24:66 (2011)
Bulatov A., Jeavons P., Krokhin A.: Classifying the complexity of constraints using finite algebras. SIAM J. Comput. 34, 720–742 (2005)
Bulín, J., Delić, D., Jackson, M., Niven, T.: On the reduction of the CSP dichotomy conjecture to digraphs. In: C. Schulte (ed.) Principles and Practice of Constraint Programming. Lecture Notes in Computer Science, vol. 8124, pp. 184–199. Springer, Berlin (2013)
Geiger D.: Closed systems of functions and predicates. Pacific J. Math. 27, 95–100 (1968)
Hell, P., Rafiey, A.: The dichotomy of list homomorphisms for digraphs. In: Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1703–1713. SIAM (2011)
Hobby, D., McKenzie, R.: The Structure of Finite Algebras. American Mathematical Society (1988)
Kearnes, K.A., Kiss, E.W.: The shape of congruence lattices. Mem. Amer. Math. Soc. 222 (2013)
Kozik M., Krokhin A., Valeriote M., Willard R.: Characterizations of several Maltsev conditions. Algebra Universalis 73, 205–224 (2015)
Larose B., Tesson P.: Universal algebra and hardness results for constraint satisfaction problems. Theoret. Comput. Sci. 410, 1629–1647 (2009)
Pöschel, R.: A general Galois theory for operations and relations and concrete characterization of related algebraic structures. Report, vol. R-01/80. Akademie der Wissenschaften der DDR, Institut für Mathematik, Berlin (1980). www.math.tu-dresden.de/~poeschel/poePUBLICATIONSpdf/poeREPORT80.pdf
Schaefer, T.J.: The complexity of satisfiability problems. In: Proceedings of the Tenth Annual ACM Symposium on Theory of Computing (STOC 1978), pp. 216–226. ACM, New York (1978)
Author information
Authors and Affiliations
Corresponding author
Additional information
Presented by M. Maroti.
Supported by the Czech-Polish cooperation grant 7AMB13PL013 “General algebra and applications” and the GAČR project 13-01832S.
Rights and permissions
About this article
Cite this article
Kazda, A. CSP for binary conservative relational structures. Algebra Univers. 75, 75–84 (2016). https://doi.org/10.1007/s00012-015-0358-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00012-015-0358-8