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arXiv · 2502.15316

Automata for Enriched Trees and Applications

Achim Blumensath
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Abstract

We study trees where each successor set is equipped with some additional structure. We introduce a family of automaton models for such trees and prove their equivalence to certain fixed-point logics. As a consequence we obtain characterisations of various variants of monadic second-order logic in terms of automata and fixed-point logics. Finally, we use our machinery to give a simplified proof of the Theorem of Muchnik and we derive several variants of this theorem for other logics.

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Achim Blumensath. 2025-02-21. Automata for Enriched Trees and Applications. https://arxiv.org/abs/2502.15316

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