4 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
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