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)


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.


Regular Expression Finite Automaton Tree Language Special Sentence Word Language 
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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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