The Determinacy of Context-Free Games
نویسندگان
چکیده
منابع مشابه
The Determinacy of Context-Free Games
We prove that the determinacy of Gale-Stewart games whose winning sets are accepted by realtime 1-counter Büchi automata is equivalent to the determinacy of (effective) analytic GaleStewart 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 ω-languages accepted by 1-counter Büchi automata is equivalent to the...
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Just as traditional games can be represented by trees, so concurrent games can be represented by event structures. We show the determinacy of such concurrent games with Borel sets of configurations as winning conditions, provided they are race-free and bounded-concurrent. Both properties are shown necessary. The determinacy proof proceeds via a reduction to the determinacy of tree games, and th...
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We prove a game theoretic dichotomy for Gδσ sets of block sequences in vector spaces that extends, on the one hand, the block Ramsey theorem of W. T. Gowers proved for analytic sets of block sequences and, on the other hand, M. Davis’ proof of Σ3 determinacy.
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We study two-player games played on the infinite graph of sentential forms induced by a contextfree grammar (that comes with an ownership partitioning of the non-terminals). The winning condition is inclusion of the derived terminal word in the language of a finite automaton. Our contribution is a new algorithm to decide the winning player and to compute her strategy. It is based on a novel rep...
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1. Preliminaries: (a) The games. (b) Extenders, iteration trees. (c) Auxiliary game representations. (d) Example: Σ 1 2 determinacy. 2. Games of length ω · ω with Σ 1 2 payoff. 3. Continuously coded games with Σ 1 2 payoff.
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2013
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl.7804050