Monadic second-order logic and linear orderings of finite structures
We consider graphs in which it is possible to specify linear orderings of the sets of vertices, in uniform ways, by MS (i.e., Monadic Second-order) formulas. We also consider classes of graphs ℂ such that for every L\(\subseteq\)ℂ, L is recognizable iff it is MS-definable. Our results concern in particular dependency graphs of partially commutative words.
KeywordsLinear Order Dependency Graph Regular Language Finite Graph Topological Sorting
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