Number conserving cellular automata: form decidability to dynamics

TL;DR

This paper establishes the equivalence of various definitions of number-conserving cellular automata, provides a linear-time decision algorithm, and classifies their dynamical behavior with an emphasis on chaoticity.

Contribution

It proves the equivalence of different definitions, offers a linear-time decision algorithm, and classifies the dynamics of number-conserving cellular automata.

Findings

All definitions of number-conserving cellular automata are equivalent.

A linear-time algorithm for deciding number-conservation is developed.

A classification of the dynamical behavior focusing on chaoticity is provided.

Abstract

We compare several definitions for number-conserving cellular automata that we prove to be equivalent. A necessary and sufficient condition for \cas to be number-conserving is proved. Using this condition, we give a linear-time algorithm to decide number-conservation. The dynamical behavior of number-conserving \cas is studied and a classification that focuses on chaoticity is given.