A Complexity Approach to Tree Algebras: the Polynomial Case - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2022

A Complexity Approach to Tree Algebras: the Polynomial Case

Résumé

In this paper, we consider infinitely sorted tree algebras recognising regular language of finite trees. We pursue their analysis under the angle of their asymptotic complexity, i.e. the asymptotic size of the sorts as a function of the number of variables involved. Our main result establishes an equivalence between the languages recognised by algebras of polynomial complexity and the languages that can be described by nominal word automata that parse linearisation of the trees. On the way, we show that for such algebras, having polynomial complexity corresponds to having uniformly boundedly many orbits under permutation of the variables, or having a notion of bounded support (in a sense similar to the one in nominal sets). We also show that being recognisable by an algebra of polynomial complexity is a decidable property for a regular language of trees.
Fichier principal
Vignette du fichier
LIPIcs-MFCS-2022-37.pdf (844.68 Ko) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte

Dates et versions

hal-03820478 , version 1 (19-10-2022)

Identifiants

Citer

Thomas Colcombet, Arthur Jaquard. A Complexity Approach to Tree Algebras: the Polynomial Case. 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022), Aug 2022, Vienna, Austria. pp.1868-8969, ⟨10.4230/LIPIcs.MFCS.2022.37⟩. ⟨hal-03820478⟩
16 Consultations
21 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More