Chen, Hubie and Marx, Dániel (2013) Block-sorted quantified conjunctive queries. In: Automata, Languages, and Programming. 40th International Colloquium, ICALP 2013, Riga, Latvia, July 8-12, 2013, Proceedings, Part II. Lecture Notes in Computer Science (7966). Springer-Verlag Wien, Berlin, pp. 125-136. ISBN 978-3-642-39211-5 10.1007/978-3-642-39212-2_14

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Abstract

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. © 2013 Springer-Verlag.

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