1,105 research outputs found
Algebraic recognizability of regular tree languages
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
Sigma-algebra or minimal tree automaton, but adds new expressivity to it. The
main result in this paper is a variety theorem \`{a} 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 S\'{e}goufin, 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
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