Algebraic recognizability of regular tree languages

Zoltán Ésik, Pascal Weil

Research output: Contribution to journalArticle

17 Citations (Scopus)


We propose a new algebraic framework to discuss and classify recognizable tree languages, and to characterize interesting classes of such languages. Our algebraic tool, called preclones, encompasses the classical notion of syntactic Σ-algebra or minimal tree automaton, but adds new expressivity to it. The main result in this paper is a variety theorem à la Eilenberg, but we also discuss important examples of logically defined classes of recognizable tree languages, whose characterization and decidability was established in recent papers (by Benedikt and Ségoufin, and by Bojańczyk and Walukiewicz) and can be naturally formulated in terms of pseudovarieties of preclones. Finally, this paper constitutes the foundation for another paper by the same authors, where first-order definable tree languages receive an algebraic characterization.

Original languageEnglish
Pages (from-to)291-321
Number of pages31
JournalTheoretical Computer Science
Issue number2
Publication statusPublished - Jun 27 2005


  • Preclones
  • Pseudovariety
  • Recognizability
  • Regular tree languages
  • Variety theorem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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