Abstract
The absorption theory of Barto and Kozik has proven to be a very useful tool in the algebraic approach to the Constraint Satisfaction Problem and the structure of finite algebras in general. We address the following problem: Given a finite relational structure \({\mathbb{A}}\) and a subset \({B \subseteq A}\), is it decidable whether B is an absorbing subuniverse? We provide an affirmative answer in the case when \({\mathbb{A}}\) has bounded width (i.e., the algebra of polymorphisms of \({\mathbb{A}}\) generates a congruence meet semidistributive variety). As a by-product, we confirm that in this case the notion of Jónsson absorption coincides with the usual absorption. We also show that several open questions about absorption in relational structures can be reduced to digraphs.
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Presented by M. Maróti.
This research was supported by the grant projects GAČR 201/09/H012, GA UK 67410, SVV-2012-265317 and the Fields Institute for Research in Mathematical Sciences.
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Bulín, J. Decidability of absorption in relational structures of bounded width. Algebra Univers. 72, 15–28 (2014). https://doi.org/10.1007/s00012-014-0283-2
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DOI: https://doi.org/10.1007/s00012-014-0283-2