Automata for Enriched Trees and Applications
Logic in Computer Science
2025-02-24 v1
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.
Cite
@article{arxiv.2502.15316,
title = {Automata for Enriched Trees and Applications},
author = {Achim Blumensath},
journal= {arXiv preprint arXiv:2502.15316},
year = {2025}
}