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Article 9, Publication date: February 2014
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An n! lower bound on formula sizeProceedings 16th Annual IEEE Symposium on Logic in Computer Science
On the Complexity of Existential Positive Queries HUBIE CHEN, Universidad del Pa´s Vasco and IKERBASQUE, Basque Foundation for Science i 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
ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery
Published: Feb 1, 2014
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