A pair of universal sequence-set betting strategies
Data Structures and Algorithms
2015-12-23 v9 Computational Complexity
Abstract
We introduce the sequence-set betting game, a generalization of An. A. Muchnik's non-monotonic betting game. Instead of successively partitioning the infinite binary strings by their value of a bit at a chosen position, as in the non-monotonic game, the player is allowed to partition the strings into any two clopen sets with equal measure. We show that, while there is no single computable sequence-set betting strategy that predicts all non-Martin-L\"of random strings, we can construct two strategies such that every non-Martin-L\"of random string is predicted by at least one of them.
Keywords
Cite
@article{arxiv.1210.5968,
title = {A pair of universal sequence-set betting strategies},
author = {Tomislav Petrović},
journal= {arXiv preprint arXiv:1210.5968},
year = {2015}
}