Projection for Büchi Tree Automata with Constraints between Siblings

Abstract

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.