Computing by nowhere increasing complexity
Information Theory
2017-10-05 v1 math.IT
Cellular Automata and Lattice Gases
Abstract
A cellular automaton is presented whose governing rule is that the Kolmogorov complexity of a cell's neighborhood may not increase when the cell's present value is substituted for its future value. Using an approximation of this two-dimensional Kolmogorov complexity the underlying automaton is shown to be capable of simulating logic circuits. It is also shown to capture trianry logic described by a quandle, a non-associative algebraic structure. A similar automaton whose rule permits at times the increase of a cell's neighborhood complexity is shown to produce animated entities which can be used as information carriers akin to gliders in Conway's game of life.
Cite
@article{arxiv.1710.01654,
title = {Computing by nowhere increasing complexity},
author = {Bar Y. Peled and Vikas K. Mishra and Avishy Y. Carmi},
journal= {arXiv preprint arXiv:1710.01654},
year = {2017}
}