2025/02/21 by Blumensath, Achim
#FOS: Computer and information sciences #Logic in Computer Science (cs.LO)
paper · doi:10.48550/arxiv.2502.15316
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.