Discrete Mathematics - Algebraic graph theory; a volume dedicated to Gert Sabidussi
On the complexity of bounded-variable queries (extended abstract)
PODS '95 Proceedings of the fourteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
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
When is the evaluation of conjunctive queries tractable?
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
Query evaluation via tree-decompositions
Journal of the ACM (JACM)
Constraint Satisfaction, Bounded Treewidth, and Finite-Variable Logics
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Preprocessing of intractable problems
Information and Computation
An n! lower bound on formula size
ACM Transactions on Computational Logic (TOCL)
Optimal implementation of conjunctive queries in relational data bases
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
On preservation under homomorphisms and unions of conjunctive queries
Journal of the ACM (JACM)
The complexity of homomorphism and constraint satisfaction problems seen from the other side
Journal of the ACM (JACM)
Homomorphism preservation theorems
Journal of the ACM (JACM)
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
Tractable Structures for Constraint Satisfaction with Truth Tables
Theory of Computing Systems
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 systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted to fall into the set; a natural question is then to classify which sentence sets are tractable and which are intractable. With respect to fixed-parameter tractability, we give a general theorem that reduces this classification question to the corresponding question for primitive positive logic, for a variety of representations of structures. This general theorem allows us to deduce that an existential positive sentence set having bounded arity is fixed-parameter tractable if and only if each sentence is equivalent to one in bounded-variable logic. We then use the lens of classical complexity to study these fixed-parameter tractable sentence sets. We show that such a set can be NP-complete, and consider the length needed by a translation from sentences in such a set to bounded-variable logic; we prove superpolynomial lower bounds on this length using the theory of compilability, obtaining an interesting type of formula size lower bound. Overall, the tools, concepts, and results of this article set the stage for the future consideration of the complexity of model checking on more expressive logics.