Martin—Löf (ML)-reducibility compares the complexity of K-trivial sets of natural numbers by examining the Martin—Löf random sequences that compute them. One says that a K-trivial set A is ML-reducible to a K-trivial set B if every ML-random computing B also computes A. We show that every K-trivial set is computable from a c.e. set of the same ML-degree. We investigate the interplay between ML-reducibility and cost functions, which are used to both measure the number of changes in a computable approximation, and the type of null sets intended to capture ML-random sequences. We show that for every cost function there is a c.e. set that is ML-complete among the sets obeying it. We characterise the K-trivial sets computable from a fragment of the left-c.e. random real Ω given by a computable set of bit positions. This leads to a new characterisation of strong jump-traceability.

Martin-Löf (ML)-可约性通过检查计算K平凡自然数集的 Martin-Löf 随机序列来比较它们的复杂性。有人说，如果每个 ML 随机计算B也计算A ，则K平凡集A可以ML简化为 K 平凡集B。我们证明每个K平凡集都可以从相同 ML 度的 ce 集计算出来。我们研究了 ML 可归约性和成本函数之间的相互作用，这些函数用于测量可计算近似值中的变化数量，以及旨在捕获 ML 随机序列的空集类型。我们证明，对于每个成本函数，在服从它的集合中，都有一个 ML 完备的 ce 集合。我们描述了可从由一组可计算的位位置给出的 left-ce 随机实数 Ω 的片段计算的K平凡集。这导致了强跳跃可追踪性的新特征。