Games with Winning Conditions of High Borel Complexity

Olivier Serre (1)

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

We first consider in nite two-player games on pushdown graphs. In previous work, Cachat, Duparc and Thomas [4] have presented a winning decidable condition that is SIgma_3-complete in the Borel hierarchy. This was the first example of a decidable winning condition of such Borel complexity. We extend this result by giving a family of decidable winning conditions of arbitrary high finite Borel complexity. From this family, we deduce a family of decidable winning conditions of arbitrary finite Borel complexity for games played on finite graphs. The problem of deciding the winner for these winning conditions is shown to be non-elementary complete.

Mots clés: Pushdown Automata; Two-player Games; Borel Complexity

Domaines: Informatique et langage [cs.CL]

Olivier Serre. Games with Winning Conditions of High Borel Complexity. Automata, Languages and Programming: 31st International Colloquium, ICALP 2004, Turku, Finland, July 12-16, 2004, 2004, Turku, Finland. pp.1150-1162. ⟨hal-00012134⟩