Decidability of the Theory of the Totally Unbounded omega-Layered Structure

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 address the decision problem for a system of monadic second-order logic interpreted over an omega-layered temporal structure devoid of both a finest layer and a coarsest one (we call such a structure totally unbounded). We propose an automaton-theoretic method that solves the problem in two steps: first, we reduce the considered problem to the problem of determining, for any given Rabin tree automaton, whether it accepts a fixed vertex-colored tree; then, we exploit a suitable notion of tree equivalence to reduce the latter problem to the decidable case of regular trees.

Domaines: Logique en informatique [cs.LO]

Angelo Montanari, Gabriele Puppis. Decidability of the Theory of the Totally Unbounded omega-Layered Structure. 11th International Symposium on Temporal Representation and Reasoning (TIME), 2004, quebec, Canada. pp.156-160. ⟨hal-00878419⟩