On Kolmogorov Complexity of Random Very Long Braided Words
Abstract
Any positive word comprised of random sequence of tokens form a finite alphabet can be reduced (without change of length) using an appropriate size Braid group relationships. Surprisingly the Braid relations dramatically reduce the Kolmogorov Complexity of the original random word and do so in distinct bands of (rate of change) values with gaps in between. Distribution of these bands are estimated and empirical statistics collected by actually coding approximations to the Kolmogorov Complexity (in Mathematica 9.0). Lempel-Ziv-Welch lossless compression algorithm techniques used to estimate the distribution for gaped bands. Evidence provided that such distributions of reduction in Kolmogorov Complexity based upon Braid groups are universal i.e. they can model more general algebraic structures other than Braid groups.
Keywords
Cite
@article{arxiv.1308.0211,
title = {On Kolmogorov Complexity of Random Very Long Braided Words},
author = {Dara O Shayda},
journal= {arXiv preprint arXiv:1308.0211},
year = {2013}
}
Comments
Additional code for v2 included in the references. Multi-pass experiments included and some test code to make sure the code is correct. The Many-Pass reductions are shown to have Gamma/Poisson distribution which has been a great excitement