整数值鞅有多强大？
How powerful are integer-valued martingales?
摘要：
在算法随机性理论中，核心概念之一是可计算随机性。一个无限二进制序列X是可计算随机的，如果没有递归鞅（策略）可以通过对X的比特值下注而赢得无限多的钱。在经典模型中，所考虑的鞅是实值的，也就是说，鞅所下的赌注可以是任意实数。本文研究了一个更严格的模型，其中只考虑整数值鞅，并研究了由该模型诱导的随机序列类。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
