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Bienvenu L.♦, Delle Rose V.♦, Steifer T., Probabilistic vs deterministic gamblers,
STACS 2022, 39th International Symposium on Theoretical Aspects of Computer Science, 2022-03-15/03-18, Marseille (FR), DOI: 10.4230/LIPIcs.STACS.2022.11, pp.11-1-13, 2022 Abstract:
Can a probabilistic gambler get arbitrarily rich when all deterministic gamblers fail? We study this problem in the context of algorithmic randomness, introducing a new notion – almost everywhere computable randomness. A binary sequence X is a.e. computably random if there is no probabilistic computable strategy which is total and succeeds on X for positive measure of oracles. Using the fireworks technique we construct a sequence which is partial computably random but not a.e. computably random. We also prove the separation between a.e. computable randomness and partial computable randomness, which happens exactly in the uniformly almost everywhere dominating Turing degrees. Keywords:
algorithmic randomness, martingales, probabilistic computation, almost everywhere domination Affiliations:
| Bienvenu L. | - | Université de Bordeaux (FR) | | Delle Rose V. | - | University of Siena (IT) | | Steifer T. | - | IPPT PAN |
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