Danny Rorabaugh ; Claude Tardif ; David Wehlau - Logical compactness and constraint satisfaction problems

lmcs:2603 - Logical Methods in Computer Science, January 23, 2017, Volume 13, Issue 1 - https://doi.org/10.23638/LMCS-13(1:1)2017
Logical compactness and constraint satisfaction problems

Authors: Danny Rorabaugh ; Claude Tardif ; David Wehlau

    We investigate a correspondence between the complexity hierarchy of constraint satisfaction problems and a hierarchy of logical compactness hypotheses for finite relational structures. It seems that the harder a constraint satisfaction problem is, the stronger the corresponding compactness hypothesis is. At the top level, the NP-complete constraint satisfaction problems correspond to compactness hypotheses that are equivalent to the ultrafilter axiom in all the cases we have investigated. At the bottom level, the simplest constraint satisfaction problems correspond to compactness hypotheses that are readily provable from the axioms of Zermelo and Fraenkel.


    Volume: Volume 13, Issue 1
    Published on: January 23, 2017
    Accepted on: January 23, 2017
    Submitted on: January 23, 2017
    Keywords: Mathematics - Logic,03E65, 68Q19

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