Separations of Non-monotonic Randomness Notions

Laurent Bienvenu, Rupert HöLzl, Thorsten KräLing & Wolfgang Merkle
In the theory of algorithmic randomness, several notions of random sequence are defined via a game-theoretic approach, and the notions that received most attention are perhaps Martin-L\"of randomness and computable randomness. The latter notion was introduced by Schnorr and is rather natural: an infinite binary sequence is computably random if no total computable strategy succeeds on it by betting on bits in order. However, computably random sequences can have properties that one may consider to...