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Cost Automata, Safe Schemes, and Downward Closures

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Barozzini D. , Clemente L. , Colcombet T. , Parys P.

2022

tom Vol. 188, nr 3

127--178

In this work we prove decidability of the model-checking problem for safe recursion schemes against properties defined by alternating B-automata. We then exploit this result to show how to compute downward closures of languages of finite trees recognized by safe recursion schemes. Higher-order recursion schemes are an expressive formalism used to define languages of finite and infinite ranked trees by means of fixed points of lambda terms. They extend regular and context-free grammars, and are equivalent in expressive power to the simply typed λY-calculus and collapsible pushdown automata. Safety in a syntactic restriction which limits their expressive power. The class of alternating B-automata is an extension of alternating parity automata over infinite trees; it enhances them with counting features that can be used to describe boundedness properties