Necessary conditions for density classification by cellular automata

Classifying the initial configuration of a binary-state cellular automaton (CA) as to whether it contains a majority of 0s or 1s—the so-called density-classification problem—has been studied over the past decade by researchers wishing to glean an understanding of how locally interacting systems compute global properties. In this paper we prove two necessary conditions that a CA must satisfy in order to classify density: (1) the density of the initial configuration must be conserved over time, and (2) the rule table must exhibit a density of 0.5.