Stochastic Cellular Automata Solve the Density Classification Problem with an Arbitrary Precision

The density classification problem consists in using a binary cellular automaton (CA) to decide whether an initial configuration contains more 0s or 1s. This problem is known for having no exact solution in the case of binary, deterministic, one-dimensional CA. Stochastic cellular automata have been studied as an alternative for solving the problem. This paper is aimed at presenting techniques to analyse the behaviour of stochastic CA rules, seen as a "blend" of deterministic CA rules. Using analytical calculations and numerical simulations, we analyse two previously studied rules and present a new rule. We estimate their quality of classification and their average time of classification. We show that the new rule solves the problem with an arbitrary precision. From a practical point of view, this rule is effective and exhibits a high quality of classification, even when the simulation time is kept small.