First-order properties of trees, star-free expressions, and aperiodicity
- Cite this paper as:
- 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
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.
Unable to display preview. Download preview PDF.