How far is Kolmogorov-Loveland randomness from Martin-Löf randomness?

@misc{petrovic2026kolmogorovloveland,
  title = {{How far is Kolmogorov-Loveland randomness from Martin-Löf randomness?}},
  author = {Tomislav Petrović},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13585},
  eprint = {2610.13585},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13585},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - How far is Kolmogorov-Loveland randomness from Martin-Löf randomness?
AU  - Tomislav Petrović
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13585
UR  - https://arxiv.org/abs/2610.13585
AB  - We'll call a map from basic to clopen sets of binary sequences an \textit{encoding} if it preserves uniform Lebesgue measure and the disjointedness relation. For some notion of randomness R we can ask if there is a computable encoding E such that for every non-Martin-Löf-random (non-MLR) sequence α, the sequences in E(α) are non-R. Thus we can use E and randomness test for R to construct a randomness test for MLR. We show that there is no such E for partial computable randomness (PCR), but there is one for Kolmogorov-Loveland randomness. Indeed, there is a total computable E and a pair of total computable non-monotonic betting strategies such that on every sequence in E(α) at least one of the strategies wins whenever α is non-MLR.
ER  -