Tree Languages Defined in First-Order Logic with One Quantifier Alternation
نویسندگان
چکیده
We study tree languages that can be defined in ∆2. 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 ∀∗∃∗, both formulas over the signature with the descendant relation. We provide an effective characterization of tree languages definable in ∆2. This characterization is in terms of algebraic equations. Over words, the class of word languages definable in ∆2 forms a robust class, which was given an effective algebraic characterization by Pin and Weil [11].
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عنوان ژورنال:
- Logical Methods in Computer Science
دوره 6 شماره
صفحات -
تاریخ انتشار 2008