Equivalence Constraint Satisfaction Problems

Authors Manuel Bodirsky, Michal Wrona

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Manuel Bodirsky
Michal Wrona

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Manuel Bodirsky and Michal Wrona. Equivalence Constraint Satisfaction Problems. In Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 16, pp. 122-136, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)


The following result for finite structures Gamma has been conjectured to hold for all countably infinite omega-categorical structures Gamma: either the model-complete core Delta of Gamma has an expansion by finitely many constants such that the pseudovariety generated by its polymorphism algebra contains a two-element algebra all of whose operations are projections, or there is a homomorphism f from Delta^k to Delta, for some finite k, and an automorphism alpha of Delta satisfying f(x1,...,xk) = alpha(f(x2,...,xk,x1)). This conjecture has been confirmed for all infinite structures Gamma that have a first-order definition over (Q;<), and for all structures that are definable over the random graph. In this paper, we verify the conjecture for all structures that are definable over an equivalence relation with a countably infinite number of countably infinite classes. Our result implies a complexity dichotomy (into NP-complete and P) for a family of constraint satisfaction problems (CSPs) which we call equivalence constraint satisfaction problems. The classification for equivalence CSPs can also be seen as a first step towards a classification of the CSPs for all relational structures that are first-order definable over Allen's interval algebra, a well-known constraint calculus in temporal reasoning.
  • Constraint satisfaction problems
  • universal algebra
  • model theory
  • Ram- sey theory
  • temporal reasoning
  • computational complexity


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