On the complexity of existential positive queries

Author:

Chen Hubie1

Affiliation:

1. Universidad del País Vasco and IKERBASQUE, Basque Foundation for Science, Bilbao, Spain

Abstract

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.

Funder

Spanish Project FORMALISM

Eusko Jaurlaritza

Euskal Herriko Unibertsitatea

Publisher

Association for Computing Machinery (ACM)

Subject

Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science

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