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We prove that the determinacy of Gale-Stewart games whose winning sets are infinitary rational relations accepted by 2-tape Buchi automata is equivalent to the determinacy of (effective) analytic Gale-Stewart games which is known to be a large cardinal assumption. Then we prove that winning strategies, when they exist, can be very complex, i.e. highly non-effective, in these games. We prove the same results for Gale-Stewart games with winning sets accepted by real-time 1-counter Buchi automata, then extending previous results obtained about these games. Then we consider the strenghs of determinacy for these games, and we prove that there is a transfinite sequence of 2-tape Buchi automata (respectively, of real-time 1-counter Buchi automata) $A_alpha$, indexed by recursive ordinals, such that the games $G(L(A_alpha))$ have strictly increasing strenghs of determinacy. Moreover there is a 2-tape Buchi automaton (respectively, a real-time 1-counter Buchi automaton) B such that the determinacy of G(L(B)) is equivalent to the (effective) analytic determinacy and thus has the maximal strength of determinacy. We show also that the determinacy of Wadge games between two players in charge of infinitary rational relations accepted by 2-tape Buchi automata is equivalent to the (effective) analytic determinacy, and thus not provable in ZFC.
We prove that the determinacy of Gale-Stewart games whose winning sets are accepted by real-time 1-counter Buchi automata is equivalent to the determinacy of (effective) analytic Gale-Stewart games which is known to be a large cardinal assumption. We
Some decidable winning conditions of arbitrarily high finite Borel complexity for games on finite graphs or on pushdown graphs have been recently presented by O. Serre in [ Games with Winning Conditions of High Borel Complexity, in the Proceedings of
We solve some decision problems for timed automata which were recently raised by S. Tripakis in [ Folk Theorems on the Determinization and Minimization of Timed Automata, in the Proceedings of the International Workshop FORMATS2003, LNCS, Volume 2791
Game semantics provides an interactive point of view on proofs, which enables one to describe precisely their dynamical behavior during cut elimination, by considering formulas as games on which proofs induce strategies. We are specifically intereste
We consider parity games on infinite graphs where configurations are represented by control-states and integer vectors. This framework subsumes two classic game problems: parity games on vector addition systems with states (vass) and multidimensional