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.
The author was supported by the Deutsche Forschungsgemeinschaft.
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© 1988 Springer-Verlag Berlin Heidelberg
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Heuter, U. (1988). First-order properties of trees, star-free expressions, and aperiodicity. In: Cori, R., Wirsing, M. (eds) STACS 88. STACS 1988. Lecture Notes in Computer Science, vol 294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035840
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DOI: https://doi.org/10.1007/BFb0035840
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