Algebraic characterization of logically defined tree languages

Zoltan Esik (1) , Pascal Weil (2)

1 Institute of Informatics
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We give an algebraic characterization of the tree languages that are defined by logical formulas using certain Lindström quantifiers. An important instance of our result concerns first-order definable tree languages. Our characterization relies on the usage of preclones, an algebraic structure introduced by the authors in a previous paper, and of the block product operation on preclones. Our results generalize analogous results on finite word languages, but it must be noted that, as they stand, they do not yield an algorithm to decide whether a given regular tree language is first-order definable.

Mots clés: tree languages; algebraic theory of languages; first-order logic; Lindstrom quantifiers; preclones

Domaines: Logique en informatique [cs.LO]; Logique [math.LO]

Zoltan Esik, Pascal Weil. Algebraic characterization of logically defined tree languages. International Journal of Algebra and Computation, 2010, 20, pp.195-239. ⟨hal-00173125v4⟩