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arXiv · 2004.12187

Cost Automata, Safe Schemes, and Downward Closures

David Barozzini·Lorenzo Clemente·Thomas Colcombet·Paweł Parys
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Abstract

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 $\lambda Y$-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.

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David Barozzini, Lorenzo Clemente, Thomas Colcombet, Paweł Parys. 2020-04-25. Cost Automata, Safe Schemes, and Downward Closures. https://doi.org/10.3233/fi-222145

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