Density classification performance and ergodicity of the Gacs-Kurdyumov-Levin cellular automaton model IV.

Almost four decades ago, Gacs, Kurdyumov, and Levin introduced three different cellular automata to investigate whether one-dimensional nonequilibrium interacting particle systems are capable of displaying phase transitions, and, as a byproduct, they introduced the density classification problem (the ability to classify arrays of symbols according to their initial density) in the cellular automata literature. Their model II became a well-known model in theoretical computer science and statistical mechanics. The other two models, however, did not receive much attention.