AI & ML
How far is Kolmogorov-Loveland randomness from Martin-L\"of randomness?
arXiv math.IT0 views
arXiv:2610.13585v1 Announce Type: cross Abstract: 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-L\"of-random (non-MLR) sequence $\alpha$, the sequences in $E(\alpha)$ 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 $E(\alpha)$ at least one of the strategies wins whenever $\alpha$ is non-MLR.
Source:https://arxiv.org/abs/2610.13585PreviousTri-Hybrid SWIPT with Reconfigurable Parasitic AntennasNextGPU-Based Parallel BP Decoding for Quantum LDPC Memory
Related posts

What Arconatese 3-4 Pontedera tells us about Serie D - Girone D
0dev.to Watercooler
Your AI agent got an HTTP error. Should it retry?
0dev.to Discuss
Is AI dangerous, or just misunderstood?
0dev.to Discuss
Why we price a developer tool per fix instead of per seat
0dev.to Productivity
My LLM-Powered Sidekick for Painless PR Descriptions
0dev.to Productivity
Reward-Adaptive Backtracking GFlowNet: A Technique Worth Understanding
0dev.to Productivity