Quantified constraints and containment problems

Conference paper


Chen, H., Madelaine, F. and Martin, B. 2008. Quantified constraints and containment problems. 23rd Annual IEEE Symposium on Logic in Computer Science (LICS 2008). Pittsburgh, PA, USA 24 - 27 Jun 2008 IEEE. pp. 317-328 https://doi.org/10.1109/LICS.2008.15
TypeConference paper
TitleQuantified constraints and containment problems
AuthorsChen, H., Madelaine, F. and Martin, B.
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.

Research GroupFoundations of Computing group
Conference23rd Annual IEEE Symposium on Logic in Computer Science (LICS 2008)
Page range317-328
ISSN1043-6871
ISBN
Hardcover9780769531830
PublisherIEEE
Publication dates
Print09 Jul 2008
Publication process dates
Deposited10 Jan 2013
Output statusPublished
Digital Object Identifier (DOI)https://doi.org/10.1109/LICS.2008.15
LanguageEnglish
Book title2008 23rd Annual IEEE Symposium on Logic in Computer Science
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