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Computability Aspects of Differential Games in Euclidian Spaces
We study computability-theoretic aspects of differential games. Our focus is
on pursuit and evasion games played in Euclidean spaces in the tradition of
Rado's "Lion versus Man" game. In some ways, these games can be viewed as
continuous versions of reachability games. We prove basic undecidability of
differential games, and study natural classes of pursuit-evasion games in
Euclidean spaces where the winners can win via computable strategies. The
winning strategy for Man found by Besicovitch for the traditional "Lion versus
Man" is not computable. We show how to modify it to yield a computable
non-deterministic winning strategy, and raise the question whether Man can win
in a computable and deterministic way