Regular ${D}$-length: A tool for improved prefix-stable forward Ramsey factorisations - MOVE Modélisation et Vérification - LIS Laboratoire d'Informatique et Systèmes de Marseille (UMR 7020)
Article Dans Une Revue Information Processing Letters Année : 2024

Regular ${D}$-length: A tool for improved prefix-stable forward Ramsey factorisations

Résumé

Recently, Jecker has introduced and studied the regular ${D}$-length of a monoid, as the length of its longest chain of regular ${D}$-classes. We use this parameter in order to improve the construction, originally proposed by Colcombet, of a deterministic automaton that allows to map a word to one of its forward Ramsey splits: these are a relaxation of factorisation forests that enjoy prefix stability, thus allowing a compositional construction. For certain monoids that have a small regular ${D}$-length, our construction produces an exponentially more succinct deterministic automaton. Finally, we apply it to obtain better complexity result for the problem of fast infix evaluation.
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hal-04562306 , version 1 (30-04-2024)

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Théodore Lopez, Benjamin Monmege, Jean-Marc Talbot. Regular ${D}$-length: A tool for improved prefix-stable forward Ramsey factorisations. Information Processing Letters, 2024, 187, pp.106497. ⟨10.1016/j.ipl.2024.106497⟩. ⟨hal-04562306⟩
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