A tetrachotomy for positive first-order logic without equality

Conference paper

Madelaine, F. and Martin, B. 2011. A tetrachotomy for positive first-order logic without equality. 26th Annual IEEE Symposium on Logic in Computer Science (LICS 2011). Ontario, Canada 21 - 24 Jun 2011 IEEE. pp. 311-320 https://doi.org/10.1109/LICS.2011.27
TypeConference paper
TitleA tetrachotomy for positive first-order logic without equality
AuthorsMadelaine, F. and Martin, B.
Abstract

We classify completely the complexity of evaluating positive equality-free sentences of first-order logic over a fixed, finite structure D. This problem may be seen as a natural generalisation of the quantified constraint satisfaction problem QCSP(D). We obtain a tetrachotomy for arbitrary finite structures: each problem is either in L, is NP-complete, is co-NP-complete or is P space-complete. Moreover, its complexity is characterised algebraically in terms of the presence or absence of specific surjective hyper-endomorphisms, and, logically, in terms of relativisation properties with respect to positive equality-free sentences. We prove that the meta-problem, to establish for a specific D into which of the four classes the related problem lies, is NP-hard.

Research GroupFoundations of Computing group
Conference26th Annual IEEE Symposium on Logic in Computer Science (LICS 2011)
Page range311-320
ISBN
Hardcover9781457704512
PublisherIEEE
Publication dates
Print2011
Publication process dates
Deposited16 Jan 2013
Output statusPublished
Additional information

Conference details: 26th Annual IEEE Symposium on Logic in Computer Science (LICS 2011), Ontario, Canada, 21-24 June 2011. Proceedings online ISBN: 9780769544120

Digital Object Identifier (DOI)https://doi.org/10.1109/LICS.2011.27
LanguageEnglish
Book titleLogic in Computer Science (LICS), 2011 26th Annual IEEE Symposium on
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