Weisfeiler-Leman Invariant Promise Valued CSPs

Authors Libor Barto , Silvia Butti

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Author Details

Libor Barto
  • Department of Algebra, Faculty of Mathematics and Physics, Charles University, Prague, Czechia
Silvia Butti
  • Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain


The authors are grateful to Victor Dalmau for his valuable comments.

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Libor Barto and Silvia Butti. Weisfeiler-Leman Invariant Promise Valued CSPs. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 4:1-4:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


In a recent line of work, Butti and Dalmau have shown that a fixed-template Constraint Satisfaction Problem is solvable by a certain natural linear programming relaxation (equivalent to the basic linear programming relaxation) if and only if it is solvable on a certain distributed network, and this happens if and only if its set of Yes instances is closed under Weisfeiler-Leman equivalence. We generalize this result to the much broader framework of fixed-template Promise Valued Constraint Satisfaction Problems. Moreover, we show that two commonly used linear programming relaxations are no longer equivalent in this broader framework.

Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
  • Promise Valued Constraint Satisfaction Problem
  • Linear programming relaxation
  • Distributed algorithms
  • Symmetric fractional polymorphisms
  • Color refinement algorithm


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