Computing by nowhere increasing complexity

TL;DR

This paper introduces a cellular automaton governed by a rule that prevents the increase of local Kolmogorov complexity, enabling it to simulate logic circuits and model algebraic structures, with variants producing dynamic information carriers.

Contribution

It presents a novel cellular automaton rule based on Kolmogorov complexity constraints, demonstrating capabilities in logic simulation and algebraic structure modeling.

Findings

Automaton can simulate logic circuits.

Automaton captures ternary logic via quandle structures.

Variants produce dynamic information carriers like gliders.

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.