A Galois connection for weighted (relational) clones of infinite size

Journal article

A Galois connection between clones and relational clones on a fixed finite domain is one of the cornerstones of the so-called algebraic approach to the computational complexity of non-uniform Constraint Satisfaction Problems (CSPs). Cohen et al. established a Galois connection between finitely-generated weighted clones and finitely-generated weighted relational clones [SICOMP’13], and asked whether this connection holds in general. We answer this question in the affirmative for weighted (relational) clones with real weights and show that the complexity of the corresponding valued CSPs is preserved.

Authors: Fulla, P; Zivny, S

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Association for Computing Machinery
• Journal: ACM Transactions on Computation Theory
• Volume: 8
• Issue: 3
• Article number: 9
• Publication date: 2015-01-01
• DOI: 10.1145/2898438
• EISSN: 1942-3462
• ISSN: 1942-3454
• Keywords: Galois connection; universal algebra; valued constraint satisfaction problems; weighted polymorphisms; discrete optimisation