On Redundancy in Constraint Satisfaction Problems

Author Clément Carbonnel

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Clément Carbonnel
  • CNRS, LIRMM, University of Montpellier, France

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Clément Carbonnel. On Redundancy in Constraint Satisfaction Problems. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


A constraint language Γ has non-redundancy f(n) if every instance of CSP(Γ) with n variables contains at most f(n) non-redundant constraints. If Γ has maximum arity r then it has non-redundancy O(n^r), but there are notable examples for which this upper bound is far from the best possible. In general, the non-redundancy of constraint languages is poorly understood and little is known beyond the trivial bounds Ω(n) and O(n^r). In this paper, we introduce an elementary algebraic framework dedicated to the analysis of the non-redundancy of constraint languages. This framework relates redundancy-preserving reductions between constraint languages to closure operators known as pattern partial polymorphisms, which can be interpreted as generic mechanisms to generate redundant constraints in CSP instances. We illustrate the power of this framework by deriving a simple characterisation of all languages of arity r having non-redundancy Θ(n^r).

Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
  • Mathematics of computing → Discrete mathematics
  • Constraint satisfaction problem
  • redundancy
  • universal algebra
  • extremal combinatorics


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