How powerful are integer-valued martingales?

Authors:
Laurent Bienvenu;Frank Stephan;Jason Teutsch
Affiliations:
LIAFA, CNRS & Université de Paris 7, France;National University of Singapore;Center for Communications Research-La Jolla
Venue:
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Year:
2010

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Abstract

In the theory of algorithmic randomness, one of the central notions is that of computable randomness. An infinite binary sequence X is computably random if no recursive martingale (strategy) can win an infinite amount of money by betting on the values of the bits of X. In the classical model, the martingales considered are real-valued, that is, the bets made by the martingale can be arbitrary real numbers. In this paper, we investigate a more restricted model, where only integer-valued martingales are considered, and we study the class of random sequences induced by this model.