Absorbing subalgebras, cyclic terms, and the Constraint Satisfaction Problem

Logical Methods in Computer Science

Volumn 8, Issue 1, 2012, Pages

  Barto, Libor ^a,b   Kozik, Marcin ^c  

^a CHARLES UNIVERSITY   (Czech Republic)

^b MCMASTER UNIVERSITY   (Canada)

^c JAGIELLONIAN UNIVERSITY   (Poland)

Author keywords

Absorbing subalgebra; Constraint Satisfaction Problem; Cyclic term; Taylor variety

Indexed keywords

EID: 84860015335     PISSN: None     EISSN: 18605974     Source Type: Journal    
DOI: 10.2168/LMCS-8(1:07)2012     Document Type: Article

References (29)

1. Libor Barto. The dichotomy for conservative constraint satisfaction problems revisited. In Proceedings of the 26th Annual IEEE Symposium on Logic in Computer Science, LICS 2011, June 21-24, 2011, Toronto, Ontario, Canada, pages 301-310. IEEE Computer Society, 2011.
2. Andrei Bulatov and Victor Dalmau. A simple algorithm for Mal'tsev constraints. SIAM J. Comput., 36(1): 16-27 (electronic), 2006.
3. Jorgen Bang-Jensen and Pavol Hell. The effect of two cycles on the complexity of colourings by directed graphs. Discrete Appl. Math., 26(1): 1-23, 1990.
4. Andrei Bulatov, Peter Jeavons, and Andrei Krokhin. Classifying the complexity of constraints using finite algebras. SIAM J. Comput., 34(3): 720-742 (electronic), 2005.
5. Libor Barto and Marcin Kozik. Congruence distributivity implies bounded width. SIAM Journal on Computing, 39(4): 1531-1542, 2009.
6. Libor Barto and Marcin Kozik. Constraint satisfaction problems of bounded width. In FOCS'09: Proceedings of the 50th Symposium on Foundations of Computer Science, pages 595-603, 2009.
7. Libor Barto and Marcin Kozik. Cyclic terms for SDV varieties revisited. Algebra Universalis, 64(1-2): 137-142, 2010.
8. Andrei A. Bulatov, Andrei A. Krokhin, and Peter Jeavons. Constraint satisfaction problems and finite algebras. In Automata, languages and programming (Geneva, 2000), volume 1853 of Lecture Notes in Comput. Sci., pages 272-282. Springer, Berlin, 2000.
9. V. G. Bodnarčuk, L. A. Kalužnin, V. N. Kotov, and B. A. Romov. Galois theory for Post algebras. I, II. Kibernetika (Kiev), (3): 1-10. 1969.
10. Libor Barto, Marcin Kozik, Miklós Maróti, Ralph McKenzie, and Todd Niven. Congruence modularity implies cyclic terms for finite algebras. Algebra Universalis, 61(3): 365-380, 2009.
11. Libor Barto, Marcin Kozik, and Todd Niven. The CSP dichotomy holds for digraphs with no sources and no sinks (a positive answer to a conjecture of Bang-Jensen and Hell). SIAM J. Comput., 38(5): 1782-1802, 2008/09.
12. Libor Barto, Marcin Kozik, and Todd Niven. Graphs, polymorphisms and the complexity of homomorphism problems. In STOC '08: Proceedings of the 40th annual ACM symposium on Theory of computing, pages 789-796, New York, NY, USA, 2008. ACM.
13. Stanley N. Burris and H. P. Sankappanavar. A course in universal algebra, volume 78 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1981.
14. Andrei A. Bulatov. Tractable conservative constraint satisfaction problems. In 18th IEEE Symposium on Logic in Computer Science (LICS 2003), 22-25 June 2003, Ottawa, Canada, Proceedings, pages 321-. IEEE Computer Society, 2003.
15. Andrei A. Bulatov. A dichotomy theorem for constraint satisfaction problems on a 3-element set. J. ACM, 53(1): 66-120 (electronic), 2006.
16. Andrei A. Bulatov. Complexity of conservative constraint satisfaction problems. ACM Trans. Comput. Logic, 12: 24: 1-24: 66, July 2011.
17. Víctor Dalmau. Generalized majority-minority operations are tractable. Log. Methods Comput. Sci., 2(4): 4: 1, 14, 2006.
18. Tomás Feder and Moshe Y. Vardi. The computational structure of monotone monadic SNP and constraint satisfaction: a study through Datalog and group theory. SIAM J. Comput., 28(1): 57-104 (electronic), 1999.
19. David Geiger. Closed systems of functions and predicates. Pacific J. Math., 27: 95-100, 1968.
20. David Hobby and Ralph McKenzie. The structure of finite algebras, volume 76 of Contemporary Mathematics. American Mathematical Society, Providence, RI, 1988.
21. Pavol Hell and Jaroslav Nešetřil. On the complexity of H-coloring. J. Combin. Theory Ser. B, 48(1): 92-110, 1990.
22. Pawel M. Idziak, Petar Markovic, Ralph McKenzie, Matthew Valeriote, and Ross Willard. Tractability and learnability arising from algebras with few subpowers. In LICS, pages 213-224. IEEE Computer Society, 2007.
23. Peter Jeavons, David Cohen, and Marc Gyssens. Closure properties of constraints. J. ACM, 44(4): 527-548, 1997.
24. Gábor Kun and Mario Szegedy. A new line of attack on the dichotomy conjecture. In Proceedings of the 41st annual ACM symposium on Theory of computing, STOC '09, pages 725-734, New York, NY, USA, 2009. ACM.
25. Miklaós Maraóti and Ralph McKenzie. Existence theorems for weakly symmetric operations. Algebra Universalis, 59(3-4): 463-489, 2008.
26. Thomas J. Schaefer. The complexity of satisfiability problems. In Conference Record of the Tenth Annual ACM Symposium on Theory of Computing (San Diego, Calif., 1978), pages 216-226. ACM, New York, 1978.
27. Mark H. Siggers. A strong mal'cev condition for locally finite varieties omitting the unary type. Algebra Universalis, 64(1-2): 15-20, 2010.
28. Walter Taylor. Varieties obeying homotopy laws. Canad. J. Math., 29(3): 498-527, 1977.
29. Matt Valeriote. personal communication.