We consider an extension of tree automata on infinite trees that can use equality and disequality constraints between direct subtrees of a node. Recently, it has been shown that the emptiness problem for these kind of automata with a parity acceptance condition is decidable and that the corresponding class of languages is closed under Boolean operations. In this paper, we show that the class of languages recognizable by such tree automata with a Büchi acceptance condition is closed under projection. This construction yields a new algorithm for the emptiness problem, implies that a regular tree is accepted if the language is non-empty (for the Büchi condition), and can be used to obtain a decision procedure for an extension of monadic second-order logic with predicates for subtree comparisons.

中文翻译：

---

兄弟间约束的 Büchi 树自动机的投影

我们考虑树自动机在无限树上的扩展，它可以在节点的直接子树之间使用相等和不相等约束。最近，已经证明这种具有奇偶接受条件的自动机的空性问题是可判定的，并且相应的语言类在布尔运算下是封闭的。在本文中，我们展示了这种具有 Büchi 接受条件的树自动机可识别的语言类在投影下是封闭的。这种构造为空性问题产生了一种新算法，意味着如果语言非空（对于 Büchi 条件），则接受常规树，并且可用于获得一元二阶逻辑扩展的决策过程带有用于子树比较的谓词。