Abstract
The Galois connection between clones and and co-clones has received a lot of attention in the context of complexity considerations for constraint satisfaction problems. However, it fails if we are interested in a reduction giving equivalence instead of only satisfiability-equivalence. We show how a similar Galois connection involving weaker closure operators can be applied for these problems. As an example of the usefulness of our construction, we show how to obtain very short proofs of complexity classifications in this context.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Allender, E., Bauland, M., Immerman, N., Schnoor, H., Vollmer, H.: The complexity of satisfiability problems: Refining schaefer’s theorem. In: Proceedings of the 30th International Symposium on Mathematical Foundations of Computer Science, pp. 71–82 (2005)
Alekseev, V., Voronenko, A.: On some closed classes in partial two-valued logic. Discrete Mathematics and Applications 4(5), 401–419 (1994)
Böhler, E., Creignou, N., Reith, S., Vollmer, H.: Playing with Boolean blocks, part II: Constraint satisfaction problems. SIGACT News 35(1), 22–35 (2004)
Böhler, E., Hemaspaandra, E., Reith, S., Vollmer, H.: Equivalence and isomorphism for Boolean constraint satisfaction. In: Bradfield, J.C. (ed.) CSL 2002 and EACSL 2002. LNCS, vol. 2471, pp. 412–426. Springer, Heidelberg (2002)
Bodrarchuk, V., Kaluzhnin, L., Kotov, V., Romov, B.: Galois theory for Post algebras i. Kibernetika 5(3), 1–10 (1969)
Böhler, E., Reith, S., Schnoor, H., Vollmer, H.: Bases for Boolean co-clones. Information Processing Letters 96, 59–66 (2005)
Bulatov, A.: A dichotomy theorem for constraint satisfaction problems on a 3-element set. Journal of the ACM 53(1), 66–120 (2006)
Creignou, N., Hébrard, J.: On generating all solutions of generalized satisfiability problems. Informatique Théorique et Applications/Theoretical Informatics and Applications 31(6), 499–511 (1997)
Creignou, N., Kolaitis, P., Zanuttini, B.: Preferred representations of Boolean relations. Technical Report TR05-119, Electronic Colloquium on Computational Complexity, ECCC (2005)
Creignou, N., Vollmer, H.: Boolean Constraint Satisfaction Problems. In: Creignou, N., Kolaitis, P.G., Vollmer, H. (eds.) Complexity of Constraints. LNCS, vol. 5250. Springer, Heidelberg (2008)
Geiger, D.: Closed systems of functions and predicates. Pac. J. Math. 27(1), 95–100 (1968)
Jeavons, P.: On the algebraic structure of combinatorial problems. Theoretical Computer Science 200, 185–204 (1998)
Ladner, R.: On the structure of polynomial-time reducibility. Journal of the ACM 22, 155–171 (1975)
Lau, D.: Function Algebras on Finite Sets: Basic Course on Many-Valued Logic and Clone Theory (Springer Monographs in Mathematics). Springer, New York (2006)
Post, E.: The two-valued iterative systems of mathematical logic. Annals of Mathematical Studies 5, 1–122 (1941)
Romov, B.: The algebras of partial functions and their invariants. Cybernetics and Systems Analysis 17(2), 157–167 (1981)
Schaefer, T.: The complexity of satisfiability problems. In: Proceedings 10th Symposium on Theory of Computing, pp. 216–226. ACM Press, New York (1978)
Schnoor, H., Schnoor, I.: Enumerating all solutions for constraint satisfaction problems. In: Creignou, N., Kolaitis, P., Vollmer, H. (eds.) Complexity of Constraints, number 06401 in Dagstuhl Seminar Proceedings. Internationales Begegnungs- und Forschungszentrum fuer Informatik (IBFI), Schloss Dagstuhl, Germany (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Schnoor, H., Schnoor, I. (2008). Partial Polymorphisms and Constraint Satisfaction Problems. In: Creignou, N., Kolaitis, P.G., Vollmer, H. (eds) Complexity of Constraints. Lecture Notes in Computer Science, vol 5250. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92800-3_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-92800-3_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-92799-0
Online ISBN: 978-3-540-92800-3
eBook Packages: Computer ScienceComputer Science (R0)