157 research outputs found
Banach-Mazur Games with Simple Winning Strategies
We discuss several notions of "simple" winning strategies for
Banach-Mazur games on graphs, such as positional strategies,
move-counting or length-counting strategies, and strategies with a
memory based on finite appearance records (FAR). We investigate
classes of Banach-Mazur games that are determined via these kinds of
winning strategies.
Banach-Mazur games admit stronger determinacy results than classical
graph games. For instance, all Banach-Mazur games with omega-regular
winning conditions are positionally determined. Beyond the
omega-regular winning conditions, we focus here on Muller conditions
with infinitely many colours. We investigate the infinitary Muller
conditions that guarantee positional determinacy for Banach-Mazur
games. Further, we determine classes of such conditions that require
infinite memory but guarantee determinacy via move-counting
strategies, length-counting strategies, and FAR-strategies. We also
discuss the relationships between these different notions of determinacy
EPE 462-3 - INDUSTRIAL MACHINE VISION NOV 10.
We discuss several notions of ‘simple’ winning strategies for Banach-Mazur games on graphs, such as positional strategies, move-counting or length-counting strategies, and strategies with a memory based on finite appearance records (FAR). We investigate classes of Banach-Mazur games that are determined via these kinds of winning strategies. Banach-Mazur games admit stronger determinacy results than classical graph games. For instance, all Banach-Mazur games with ω-regular winning conditions are positionally determined. Beyond the ω-regular winning conditions, we focus here on Muller conditions with infinitely many colours. We investigate the infinitary Muller conditions that guarantee positional determinacy for Banach-Mazur games. Further, we determine classes of such conditions that require infinite memory but guarantee determinacy via move-counting strategies, length-counting strategies, and FAR-strategies. We also discuss the relationships between these different notions of determinacy
Baire spaces and infinite games
It is well known that if the nonempty player of the Banach-Mazur game has a
winning strategy on a space, then that space is Baire in all powers even in the
box topology. The converse of this implication may be true also: We know of no
consistency result to the contrary. In this paper we establish the consistency
of the converse relative to the consistency of the existence of a proper class
of measurable cardinals.Comment: 21 page
Playing Games in the Baire Space
We solve a generalized version of Church's Synthesis Problem where a play is
given by a sequence of natural numbers rather than a sequence of bits; so a
play is an element of the Baire space rather than of the Cantor space. Two
players Input and Output choose natural numbers in alternation to generate a
play. We present a natural model of automata ("N-memory automata") equipped
with the parity acceptance condition, and we introduce also the corresponding
model of "N-memory transducers". We show that solvability of games specified by
N-memory automata (i.e., existence of a winning strategy for player Output) is
decidable, and that in this case an N-memory transducer can be constructed that
implements a winning strategy for player Output.Comment: In Proceedings Cassting'16/SynCoP'16, arXiv:1608.0017
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