Decidability of MSO Theories of Tree Structures

Angelo Montanari (1) , Gabriele Puppis (2)

1 DIMI - Dipartimento di Matematica e Informatica - Universita Udine
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

In this paper we provide an automaton-based solution to the decision problem for a large set of monadic second-order theories of deterministic tree structures. We achieve it in two steps: first, we reduce the considered problem to the problem of determining, for any Rabin tree automaton, whether it accepts a given tree; then, we exploit a suitable notion of tree equivalence to reduce (a number of instances of) the latter problem to the decidable case of regular trees. We prove that such a reduction works for a large class of trees, that we call residually regular trees. We conclude the paper with a short discussion of related work.

Domaines: Théorie et langage formel [cs.FL]; Logique en informatique [cs.LO]

Angelo Montanari, Gabriele Puppis. Decidability of MSO Theories of Tree Structures. 24th Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS), 2004, Chennai, India. pp.430-442. ⟨hal-00878415⟩