The Determinacy of Context-Free Games

Abstract : 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)).
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Soumis le : lundi 5 décembre 2011 - 17:50:30
Dernière modification le : vendredi 4 janvier 2019 - 17:32:32
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Olivier Finkel. The Determinacy of Context-Free Games. 29th International Symposium on Theoretical Aspects of Computer Science, STACS 2012, 2012, Paris, France. pp.555-566, ⟨10.4230/LIPIcs.STACS.2012.555⟩. ⟨hal-00648462⟩

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