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Article Dans Une Revue Logical Methods in Computer Science Année : 2017

Algebraic and logical descriptions of generalized trees

Résumé

Quasi-trees generalize trees in that the unique "path" between two nodes may be infinite and have any countable order type. They are used to define the rank-width of a countable graph in such a way that it is equal to the least upper-bound of the rank-widths of its finite induced subgraphs. Join-trees are the corresponding directed trees. They are useful to define the modular decomposition of a countable graph. We also consider ordered join-trees, that generalize rooted trees equipped with a linear order on the set of sons of each node. We define algebras with finitely many operations that generate (via infinite terms) these generalized trees. We prove that the associated regular objects (those defined by regular terms) are exactly the ones that are the unique models of monadic second-order sentences. These results use and generalize a similar result by W. Thomas for countable linear orders.
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Dates et versions

hal-01299077 , version 1 (07-04-2016)
hal-01299077 , version 2 (03-05-2016)
hal-01299077 , version 3 (02-10-2016)

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  • HAL Id : hal-01299077 , version 3

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Bruno Courcelle. Algebraic and logical descriptions of generalized trees. Logical Methods in Computer Science, 2017, 13 (3), pp.Article 7. ⟨hal-01299077v3⟩

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