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First-order properties of trees, star-free expressions, and aperiodicity

  • Uschi Heuter
Contributed Papers Formal Languages
Part of the Lecture Notes in Computer Science book series (LNCS, volume 294)

Abstract

We characterize the first-order definable sets of finite trees in terms of appropriate star-free tree expressions and show that for sets of trees first-order definability is strictly weaker than aperiodicity. These two theorems show how far the results of McNaughton and Schützenberger on starfree sets of words (stating the equivalence between first-order definability, star-freeness, and aperiodicity) are transferable to the context of trees. Both results of the paper rely on the method of the Ehrenfeucht-Fraissé-game.

Keywords

Regular Expression Finite Automaton Tree Language Special Sentence Word Language 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Uschi Heuter
    • 1
  1. 1.Lehrstuhl für Informatik II RWTH AachenAachenWest-Germany

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