The Determinacy of Context-Free Games

Olivier Finkel (1)

1 ELM - Équipe de Logique Mathématique

We prove that the determinacy of Gale-Stewart games whose winning sets are accepted by real-time 1-counter Büchi automata is equivalent to the determinacy of (effective) analytic Gale-Stewart games which is known to be a large cardinal assumption. We show also that the determinacy of Wadge games between two players in charge of omega-languages accepted by 1-counter Büchi automata is equivalent to the (effective) analytic Wadge determinacy. Using some results of set theory we prove that one can effectively construct a 1-counter Büchi automaton A and a Büchi automaton B such that: (1) There exists a model of ZFC in which Player 2 has a winning strategy in the Wadge game W(L(A), L(B)); (2) There exists a model of ZFC in which the Wadge game W(L(A), L(B)) is not determined. Moreover these are the only two possibilities, i.e. there are no models of ZFC in which Player 1 has a winning strategy in the Wadge game W(L(A), L(B)).

Mots clés: Automata and formal languages; logic in computer science; Gale-Stewart games; Wadge games; determinacy; context-free games

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

Olivier Finkel. The Determinacy of Context-Free Games. STACS'12 (29th Symposium on Theoretical Aspects of Computer Science), Feb 2012, Paris, France. pp.555-566. ⟨hal-00678158⟩