论文标题
可计算的随机性大于概率
Computable randomness is about more than probabilities
论文作者
论文摘要
我们引入了无限序列的可计算随机性概念，该序列以两种重要方式将经典版本泛化。首先，我们对可计算随机性的定义与不精确的概率模型相关联，从某种意义上说，我们考虑较低的期望（或概率集），而不是经典的“精确”概率。其次，我们考虑了在某些有限的样品空间中元素采用值的序列，而不是二进制序列。有趣的是，我们发现每个序列都相对于至少一个较低的期望而言是随机的，并且较低信息的较低的期望值较少的随机序列较少。这导致了一个有趣的问题，每个序列对于独特的最有用的较低期望值是否是随机的。我们详细研究了这个问题，并提供了部分答案。
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.
