When is the evaluation of conjunctive queries tractable?
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Optimal implementation of conjunctive queries in relational data bases
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
The complexity of homomorphism and constraint satisfaction problems seen from the other side
Journal of the ACM (JACM)
Quantified Constraints and Containment Problems
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
The complexity of quantified constraint satisfaction problems under structural restrictions
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Tractable hypergraph properties for constraint satisfaction and conjunctive queries
Proceedings of the forty-second ACM symposium on Theory of computing
Constraint satisfaction with succinctly specified relations
Journal of Computer and System Sciences
Decomposing Quantified Conjunctive (or Disjunctive) Formulas
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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We study the complexity of model checking in quantified conjunctive logic, that is, the fragment of first-order logic where both quantifiers may be used, but conjunction is the only permitted connective. In particular, we study block-sorted queries, which we define to be prenex sentences in multi-sorted relational first-order logic where two variables having the same sort must appear in the same quantifier block. We establish a complexity classification theorem that describes precisely the sets of block-sorted queries of bounded arity on which model checking is fixed-parameter tractable. This theorem strictly generalizes, for the first time, the corresponding classification for existential conjunctive logic (which is known and due to Grohe) to a logic in which both quantifiers are present.