We study tree languages that can be defined in Δ2. These are tree languages definable by a first-order formula whose quantifier prefix is ∃*∀*, and simultaneously by a first-order formula whose quantifier prefix is ∀*∃z.ast;, both formulas over the signature with the descendant relation. We provide an effective characterization of tree languages definable in Δ2. This characterization is in terms of algebraic equations. Over words, the class of word languages definable in Δ2 forms a robust class, which was given an effective algebraic characterization by Pin and Weil [11]. © 2008 Springer-Verlag.
CITATION STYLE
Bojańczyk, M., & Segoufin, L. (2008). Tree languages defined in first-order logic with one quantifier alternation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5126 LNCS, pp. 233–245). https://doi.org/10.1007/978-3-540-70583-3_20
Mendeley helps you to discover research relevant for your work.