Computing by nowhere increasing complexity

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 automato...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2017-10
Main Authors: Peled, Bar Y, Mishra, Vikas K, Carmi, Avishy Y
Format: Article
Language:English
Subjects:
Cellular automata
Complexity
Computer simulation
Gliders
Logic circuits
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422