Tree Automata Make Ordinal Theory Easy

Thierry Cachat (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

We give a new simple proof of the decidability of the First Order Theory of (omega^omega^i,+) and the Monadic Second Order Theory of (omega^i,<), improving the complexity in both cases. Our algorithm is based on tree automata and a new representation of (sets of) ordinals by (infinite) trees.

Mots clés: ordinals; logic; first-order; second-order; tree; automata

Domaines: Informatique et théorie des jeux [cs.GT]

Thierry Cachat. Tree Automata Make Ordinal Theory Easy. 2006, pp.286-297. ⟨hal-00110485⟩