Higher-order recursion schemes are an expressive formalism used to define languages of possibly infinite ranked trees.

Higher-order recursion schemes are an expressive formalism used to define languages of possibly infinite ranked trees.

We prove, under a syntactical constraint called safety, decidability of the model-checking problem for recursion schemes against properties defined by alternating B-automata, an extension of alternating parity automata for infinite trees with a boundedness acceptance condition.
We then exploit this result to show how to compute downward closures of languages of finite trees recognized by safe recursion schemes.

This talk is based on a joint work with Lorenzo Clemente, Thomas Colcombet and Paweł Parys.