# Quantified constraints and containment problems

Chen, Hubie, Madelaine, Florent and Martin, Barnaby
(2008)
*Quantified constraints and containment problems.*
2008 23rd Annual IEEE Symposium on Logic in Computer Science.
In: 23rd Annual IEEE Symposium on Logic in Computer Science (LICS 2008), 24-27 June 2008, Pittsburgh, PA, USA.
ISBN 9780769531830.
ISSN 1043-6871
(doi:10.1109/LICS.2008.15)

## Abstract

We study two containment problems related to the quantified constraint satisfaction problem (QCSP). Firstly, we give a combinatorial condition on finite structures A and B that is necessary and sufficient to render QCSP(A) a subset of QCSP(B). The required condition is the existence of a positive integer r such that there is a surjective homomorphism from the power structure A^r to B. We note that this condition is already necessary to guarantee containment of the Pi_2 restriction of QCSP, that is Pi_2-CSP(A) a subset of Pi_2-CSP(B). Since we are able to give an effective bound on such an r, we provide a decision procedure for the model containment problem with non-deterministic double-exponential time complexity. Secondly, we prove that the entailment problem for quantified conjunctive-positive first-order logic is decidable. That is, given two sentences phi and psi of first-order logic with no instances of negation or disjunction, we give an algorithm that determines whether "phi implies psi" is true in all structures (models). Our result is in some sense tight, since we show that the entailment problem for positive first-order logic (i.e. quantified conjunctive-positive logic plus disjunction) is undecidable.

Item Type: | Conference or Workshop Item (Paper) |
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Research Areas: | A. > School of Science and Technology > Computer Science A. > School of Science and Technology > Computer Science > Foundations of Computing group |

Item ID: | 9756 |

Depositing User: | Devika Mohan |

Date Deposited: | 10 Jan 2013 06:18 |

Last Modified: | 11 Jun 2019 15:09 |

URI: | https://eprints.mdx.ac.uk/id/eprint/9756 |

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