An optimal k-consistency algorithm
Artificial Intelligence
On the expressive power of Datalog: tools and a case study
Selected papers of the 9th annual ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Some combinatorial game problems require Ω(nk) time
Journal of the ACM (JACM)
Conjunctive-query containment and constraint satisfaction
Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
A Game-Theoretic Approach to Constraint Satisfaction
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Constraint Satisfaction, Bounded Treewidth, and Finite-Variable Logics
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Equivalence in finite-variable logics is complete for polynomial time
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
The parameterized complexity of local consistency
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Parameterized Complexity
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The existential k-pebble game characterizes the expressive power of the existential-positive k-variable fragment of first-order logic on finite structures. The winner of the existential k-pebble game on two given finite structures can easily be determined in polynomial time, where the degree of the polynomial is linear in k. We show that this linear dependence on the parameter k is necessary by proving an unconditional polynomial lower bound for determining the winner in the existential k-pebble game on finite structures. Establishing strong k-consistency is a well-known heuristic for solving the constraint satisfaction problem (CSP). By the game characterization of Kolaitis and Vardi our result implies a lower bound on every algorithm that decides if strong k-consistency can be established for a given CSP-instance.