Density Classification Task
The Density Classification Task is the task in which the constituents of a Finite State Machine simultaneously assume the initial majority state given an initial random distribution of states.
One example of where the Density Classification Task can be seen is in a one-dimensional Cellular Automata model. Cells are randomly assigned a value of 0 or 1. If the majority of the cells are initially assigned 1, then the Density Classification Task has been completed when all cells have assumed a value of 1 (after a given number of generations). Inversely, if the majority of cells are initially assigned 0, then the task has been completed when all cells have assumed a value of 0. In a noisy environment (where there is a probability that two cells will miscommunicate, reporting a 1 instead of a 0 or vice versa), a simple majority rule will accomplish the task.
Applications
A Finite State Machine's ability to complete the Density Classification Task can be indicative of the interlinkage between its constituents.