Correspondence:
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Address for correspondence: Chair of Computer Science 7, RWTH Aachen University, Germany.
Abstract: Infinite games (in the form of Gale-Stewart games) are studied where a play is a sequence of natural numbers chosen by two players in alternation, the winning condition being a subset of the Baire space ω^ω. We consider such games defined by a natural kind of parity automata over the alphabet ℕ, called ℕ-MSO-automata, where transitions are specified by monadic second-order formulas over the successor structure of the natural numbers. We show that the classical Büchi-Landweber Theorem (for finite-state games in the Cantor space 2^ω) holds again for the present games: A game defined by a deterministic parity ℕ-MSO-automaton is determined, the winner can be computed, and an ℕ-MSO-transducer realizing a winning strategy for the winner can be constructed.
Keywords: infinite games, Gale-Stewart games, determinacy, automata over infinite alphabets, transducers, monadic second-order logic, Church’s synthesis problem, pushdown systems
