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References
S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases. Addison-Wesley, 1995.
M. Ajtai and Y. Gurevich. Datalog vs first-order logic. Journal of Computer and System Sciences, 49(3):562–588, 1994.
K. Apt. Principles of Constraint Programming. Cambridge Univ. Press, 2003.
S. Arnborg, D. G. Corneil, and A. Proskurowski. Complexity of finding embeddings in a k-tree. SIAM Journal of Algebraic and Discrete Methods,8:277–284, 1987.
A. Atserias. On digraph coloring problems and treewidth duality. In Proc. 20th IEEE Symp. on Logic in Computer Science, pages p106–115, 2005.
W. Bibel. Constraint satisfaction from a deductive viewpoint. Artificial Intelligence, 35:401–413, 1988.
H. L. Bodlaender. A linear-time algorithm for finding tree-decompositions of small treewidth. In Proc. 25th ACM Symp. on Theory of Computing, pages 226–234, 1993.
A. A. Bulatov. A dichotomy theorem for constraints on a three-element set. In Proc. 43rd Symp. on Foundations of Computer Science, pages 649–658, 2002.
A. A. Bulatov. Tractable conservative constraint satisfaction problems. In Proc. 18th IEEE Symp. on Logic in Computer Science, pages 321–330, 2003.
A. A. Bulatov, P. Jeavons, and A. A. Krokhin. Classifying the complexity of constraints using finite algebras. SIAM Journal on Computing, 34(3):720–742, 2005.
A. K. Chandra and P. M. Merlin. Optimal implementation of conjunctive queries in relational databases. In Proc. 9th ACM Symp. on Theory of Computing, pages 77–90, 1977.
C. Chekuri and A. Rajaraman. Conjunctive query containment revisited. In Ph.G. Kolaitis and F. Afrati, editors,Proc. 6th Int’l Conf. on Database Theory,Lecture Notes in Computer Science, volume 1186, pages 56–70. Springer, 1997.
H. Chen and V. Dalmau. Beyond hypertree width: Decomposition methods without decompositions. In Proc. 11th Int’l Conf. on Principles and Practice of Constraint Programming, Lecture Notes in Computer Science, volume 3709, pages 167–181. Springer, 2005.
D. A. Cohen, P. Jeavons, and M. Gyssens. A unified theory of structural tractability for constraint satisfaction and spread cut decomposition. In Proc. 19th Int’l Joint Conf. on Artificial Intelligence, pages 72–77, 2005.
M. C. Cooper. An optimal k-consistency algorithm. Artificial Intelligence, 41(1):89–95, 1989.
B. Courcelle, J. A. Makowsky, and U. Rotics. Linear time solvable optimization problems on graphs of bounded cliquewidth. Theory of Computing Systems, 33:125–150, 2000.
V. Dalmau. Generalized majority–minority operations are tractable. In Proc. 20th IEEE Symp. on Logic in Computer Science, pages 438–447, 2005.
V. Dalmau, Ph. G. Kolaitis, and M.Y. Vardi. Constraint satisfaction, bounded treewidth, and finite-variable logics. In P. Van Hentenryck, editor, Proc. 8th Int’l Conf. on Constraint Programming, Lecture Notes in Computer Science, volume 2470, pages 310–326. Springer, 2002.
V. Dalmau and J. Pearson. Closure functions and width 1 problems. In Proc. 5th Int’l Conf. on Principles and Practice of Constraint Programming, Lecture Notes in Computer Science, volume 1713, pages 159–173. Springer, 1999.
R. Dechter. Constraint networks. In S. C. Shapiro, editor, Encyclopedia of Artificial Intelligence, pages 276–185. Wiley, New York, 1992.
R. Dechter. From local to global consistency. Artificial Intelligence, 55(1): 87–107, May 1992.
R. Dechter. Bucket elimination: a unifying framework for reasoning. Artificial Intelligence, 113(1–2):41–85, 1999.
R. Dechter. Constraint Processing. Morgan Kaufmman, 2003.
R. Dechter and I. Meiri. Experimental evaluation of preprocessing algorithms for constraint satisfaction problems. Artificial Intelligence, 68:211–241, 1994.
R. Dechter and J. Pearl. Tree clustering for constraint networks. Artificial Intelligence, pages 353–366, 1989.
R. G. Downey and M. R. Fellows. Parametrized Complexity. Springer, 1999.
T. Feder. Constraint satisfaction: A personal perspective. Technical report, Electronic Colloquium on Computational Complexity,2006. Report TR06-021.
T. Feder and D. Ford. Classification of bipartite boolean constraint satisfaction through delta-matroid intersection. Technical report, Electronic Colloquium on Computational Complexity, 2005. Report TR05-016.
T. Feder and M. Y. Vardi. The computational structure of monotone monadic SNP and constraint satisfaction: a study through Datalog and group theory. SIAM J. on Computing, 28:57–104, 1998.
T. A. Feder and M. Y. Vardi. Monotone monadic SNP and constraint satisfaction. In Proc. 25th ACM Symp. on Theory of Computing, pages 612–622, 1993.
E. C. Freuder. Synthesizing constraint expressions. Communications of the ACM, 21(11):958–966, November 1978.
E. C. Freuder. A sufficient condition for backtrack-free search. Journal of the Association for Computing Machinery, 29(1):24–32, 1982.
E. C Freuder. Complexity of k-tree structured constraint satisfaction problems. Proc. 7th National Conference on Artificial Intelligence, pages 4–9, 1990.
D. H. Frost. Algorithms and Heuristics for Constraint Satisfaction Problems. PhD thesis, Department of Computer Science, University of California, Irvine, 1997.
H. Gaifman, H. Mairson, Y. Sagiv, and M. Y. Vardi. Undecidable optimization problems for database logic programs. In Proc. 2nd IEEE Symp. on Logic in Computer Science, pages 106–115, 1987
M. R. Garey and D. S. Johnson. Computers and Intractability - A Guide to the Theory of NP-Completeness. W. H. Freeman and Co., 1979.
G. Gottlob, N. Leone, and F. Scarcello. The complexity of acyclic conjunctive queries. In Proc. 39th IEEE Symp. on Foundation of Computer Science, pages 706–715, 1998.
G. Gottlob, N. Leone, and F. Scarcello. A comparison of structural CSP decomposition methods. In Proc. 16th Int’l Joint Conf. on Artificial Intelligence, pages 394–399, 1999.
G. Gottlob, N. Leone, and F. Scarcello. Hypertree decompositions and tractable queries. In Proc. 18th ACM Symp. on Principles of Database Systems, pages 21–32, 1999.
M. Grohe. The complexity of homomorphism and constraint satisfaction problems seen from the other side. In Proc. 44th IEEE Symp. on Foundations of Computer Science, pages 552–561, 2003.
M. Grohe, T. Schwentick, and L. Segoufin. When is the evaluation of conjunctive queries tractable? In Proc. 33rd ACM Symp. on Theory of Computing, pages 657–666, 2001.
M. Gyssens, P. G. Jeavons, and D. A. Cohen. Decomposition constraint satisfaction problems using database techniques. Artificial Intelligence, 66:57–89, 1994.
P. Hell and J. Nešetřil. On the complexity of H-coloring. Journal of Combinatorial Theory, Series B, 48:92–110, 1990.
P. Hell and J. Nešetřil. Graphs and Homomorphisms. Oxford Lecture Series in Mathematics and Its applications, No. 28. Oxford University Press, 2004.
Ph. G. Kolaitis and J. Panttaja. On the complexity of existential pebble games. In Proc. 12th Conf. Computer Science Logic, Lecture Notes in Computer Science, volume 2803, pages 314–329. Springer, 2003.
Ph. G. Kolaitis and M. Y. Vardi. The decision problem for the probabilities of higher-order properties. In Proc. 19th ACM Symp. on Theory of Computing, pages 425–435, 1987.
Ph. G. Kolaitis and M. Y. Vardi. On the expressive power of variable-confined logics. In Proc. 11th IEEE Symp. on Logic in Computer Science, pages 348–359, 1996.
Ph.G. Kolaitis and M.Y. Vardi. Conjunctive-query containment and constraint satisfaction. Journal of Computer and System Sciences, pages 302–332, 2000.
Ph.G. Kolaitis and M.Y. Vardi. A game-theoretic approach to constraint satisfaction. In Proc. of the 17th National Conference on Artificial Intelligence, pages 175–181, 2000.
V. Kumar. Algorithms for constraint-satisfaction problems. AI Magazine, 13:32–44, 1992.
R. E.—Ladner. On the structure of polynomial time reducibility. Journal of The Association for Computing Machinery, 22:155–171, 1975.
B. Larose, C. Loten, and C. Tardif. A characterisation of first-order constraint satisfaction problems. In Proc. 21st IEEE Symp. on Logic in Computer Science, pages 201–210, 2006.
L. A. Levin. Universal sorting problems. Problemy Peredaci Informacii, 9:115–116, 1973. In Russian. English translation in Problems of Information Transmission 9:265–266, 1973.
A. K. Mackworth and E. C. Freuder. The complexity of constraint satisfaction revisited. Artificial Intelligence, 59(1–2):57–62, 1993.
B. J. McMahan, G. Pan, P. Porter, and M. Y. Vardi. Projection pushing revisited. In Proc. 9th Int’l Conf. on Extending Database Technology, Lecture Notes in Computer Science, volume 2992, pages 441–458. Springer, 2004.
P. Meseguer. Constraint satisfaction problems: an overview. AI Communications, 2:3–16, 1989.
C. Papadimitriou and M. Yannakakis. Optimization, approximation and complexity classes. Journal of Computer and System Sciences, 43:425–440, 1991.
J. Pearson and P. Jeavons. A survey of tractable constraint satisfaction problems. Technical Report CSD-TR-97-15, Royal Holloway University of London, 1997.
N. Robertson and P. D. Seymour. Graph minors IV: Tree-width and well-quasi-ordering. Journal of Combinatorial Theory, Series B, 48(2):227–254, 1990.
E. Rosen. Finite Model Theory and Finite Variable Logics. Ph.D. Thesis, University of Pennsylvania, 1995.
B. Rossman. Existential positive types and preservation under homomorphisisms. In Proc. 20th IEEE Symp. on Logic in Computer Science, pages 467–476, 2005.
Y. Saraiya. Subtree Elimination Algorithms in Deductive Databases. PhD Thesis, Department of Computer Science, Stanford University, 1991.
T. J. Schaefer. The complexity of satisfiability problems. In Proc. 10th ACM Symp. on Theory of Computing, pages 216–226, 1978.
E. P. K. Tsang. Foundations of Constraint Satisfaction. Academic Press, 1993.
P. van Beek. On the inherent tightness of local consistency in constraint networks. In Proc. 11th National Conference on Artificial Intelligence, pages 368–373, 1994.
P. van Beek and R. Dechter. Constraint tightness and looseness versus local and global consistency. Journal of The Association for Computing Machinery, 44(4):549–566, 1997.
M. Y. Vardi. The complexity of relational query languages. In Proc. 14th ACM Symp. on Theory of Computing, pages 137–146, 1982.
M. Y. Vardi. On the complexity of bounded-variable queries. In Proc. 14th ACM Symp. on Principles of Database Systems, pages 266–76, 1995.
M. Yannakakis. Algorithms for acyclic database schemes. In Proc. 7 Int’l Conf. on Very Large Data Bases, pages 82–94, 1981.
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Kolaitis, P.G., Vardi, M.Y. (2007). A Logical Approach to Constraint Satisfaction. In: Finite Model Theory and Its Applications. Texts in Theoretical Computer Science an EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68804-8_6
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