Algebraic characterization of logically defined tree languages

Zoltán Ésik, Pascal Weil

Research output: Contribution to journalArticle

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)195-239
Number of pages45
JournalInternational Journal of Algebra and Computation
Issue number2
Publication statusPublished - Mar 1 2010



  • Block product
  • First-order definability
  • Lindström quantifiers
  • Preclones
  • Recognizability
  • Tree languages

ASJC Scopus subject areas

  • Mathematics(all)

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