Cost Automata, Safe Schemes, and Downward Closures [article]

David Barozzini, Lorenzo Clemente, Thomas Colcombet, Paweł Parys
2022 arXiv   pre-print
Higher-order recursion schemes are an expressive formalism used to define languages of finite and infinite ranked trees. They extend regular and context-free grammars, and are equivalent in expressive power to the simply typed λ Y-calculus and collapsible pushdown automata. In this work 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
more » ... tomata over 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.
arXiv:2004.12187v3 fatcat:dgp2l6se7rdvfnvbtc2wehzg4q