English

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.

Keywords

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}
}
R2 v1 2026-06-22T22:03:41.631Z