可计算的随机性不仅仅是概率
Computable randomness is about more than probabilities
摘要：
我们引入了一个概念，可计算的随机性无穷序列，概括了经典的版本在两个重要的方面。首先，我们对可计算随机性的定义与不精确的概率模型有关，在这个意义上，我们考虑的是较低的期望（或概率集），而不是经典的“精确”概率。其次，我们考虑的是元素在有限样本空间取值的序列，而不是二元序列。有趣的是，我们发现每个序列相对于至少一个较低的期望是可计算随机的，并且信息量更大的较低期望具有更少的可计算随机序列。这就引出了一个有趣的问题：相对于一个唯一的、信息量最大的较低期望，每个序列是否都是可计算随机的？我们对这个问题进行了一些详细的研究，并提供了部分答案。
英文摘要：
We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense that we consider lower expectations (or sets of probabilities) instead of classical 'precise' probabilities. Secondly, instead of binary sequences, we consider sequences whose elements take values in some finite sample space. Interestingly, we find that every sequence is computably random with respect to at least one lower expectation, and that lower expectations that are more informative have fewer computably random sequences. This leads to the intriguing question whether every sequence is computably random with respect to a unique most informative lower expectation. We study this question in some detail and provide a partial answer.
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