How powerful are integer-valued martingales?

Details How powerful are integer-valued martingales? How powerful are integer-valued martingales?

2010-04-06

arxiv.org/abs/1004.0838v2

Computer Science

Computer Science and Game Theory

Long version of the CiE 2010 paper.

Scientific paper

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.

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