Computational supplement to "Network Satisfaction over Four-Atom Relation Algebras: Complexity and Representations"
Year: 2026
Type: preprint
Abstract: Andréka and Maddux classified the relation algebras with at most 3 atoms, and in particular they showed that all of them are representable. Cristani and Hirsch showed that the network satisfaction problem (NSP) for each of these algebras is in P or NP-complete. The literature contains many results on representations of relation algebras; in particular, some relation algebras with four atoms are not representable. We extend the result of Cristani and Hirsch to relation algebras with at most 4 atoms: the NSP is always either in P or NP-complete. To this end, we construct universal, fully universal, or even normal representations for these algebras, whenever possible.
Source: arXiv (Cornell University)
Institution: Technische Universität Dresden
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: European Commission
Award: G1304993860
OpenAlex ID: W6979299763
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