Abstract
It is impossible to effectively modify a string in order to increase its Kolmogorov complexity. However, is it possible to construct a few strings, no longer than the input string, so that most of them have larger complexity? We show that the answer is yes. We present an algorithm that takes as input a string x of length n and returns a list with O(n2) strings, all of length n, such that 99% of them are more complex than x, provided the complexity of x is less than n−loglogn−O(1). We also present an algorithm that obtains a list of quasi-polynomial size in which each element can be produced in polynomial time.
Funder
National Science Foundation
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
Reference7 articles.
1. Universal almost optimal compression and Slepian-Wolf coding in probabilistic polynomial time;Bauwens;arXiv,2019
2. Information-theoretic characterizations of recursive infinite strings