arXiv:2606.24711 · v2

Almost Symmetric Linear Arc Monadic Datalog and Transitive Tournaments

首次提交 2026-06-23 23:33

版本更新 2026-11-04 08:09

雷达观测 2026-11-05 11:11

摘要

We introduce $n$-almost symmetric Datalog and study $n$-almost symmetric linear arc monadic Datalog. We characterize the finite relational structures whose constraint satisfaction problem is solved by this Datalog fragment as those that can be primitive positively constructed from the transitive tournament on $n+2$ vertices. We also give characterizations in terms of a certain homomorphism duality (which we call $n$-fixed unfolded caterpillar duality) and in universal-algebraic terms (the existence of $k$-absorptive operations and of operations forming an elevator chain of length $n+1$). This article generalizes the results from Bodirsky and Starke about symmetric linear arc monadic Datalog.