Algebraic recognizability of regular tree languages

  • Authors:

  • Zoltán Ésik;Pascal Weil

  • Affiliations:

  • Department of Computer Science, University of Szeged, Hungary and Research Group on Mathematical Linguistics, Rovira i Virgili University, Tarragona, Spain;LaBRI, Université Bordeaux, France and University of Nebraska in Lincoln

  • Venue:
  • Theoretical Computer Science - The art of theory
  • Year:
  • 2005

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Abstract

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 Bojanczyk 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.