K-trivial set

Known as: K-trivial sets

In mathematics, a set of natural numbers is called a K-trivial set if its initial segments viewed as binary strings are easy to describe: the prefix…

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.

2017

2017

In algorithmic randomness, the class of K-trivial sets has proved itself to be remarkable, due to its numerous different…

2017

Martin-Löf (ML)-reducibility compares K-trivial sets by examining the Martin-Löf random sequences that compute them. We show that…

2016

We study the sets that are computable from both halves of some (Martin-Löf) random sequence, which we call 1{2-bases. We show…

2014

We prove that superhigh sets can be jump traceable, answering a question of Cole and Simpson. On the other hand, we show that…

2014

The (prefix-free) Kolmogorov complexity of a finite binary string is the length of the shortest description of the string. This…

2012

Monotone complexity, Km, is a variant of Kolmogorov complexity that was introduced independently by Levin and Schnorr. The…

2010

In this chapter, we introduce an important class of “randomnesstheoretically weak” sets, the K-trivial sets. As we will see, this…

2002

We investigate combinatorial lowness properties of sets of natural numbers (reals). The real A is super-low if A′ ≤tt ∅′, and A…