Information Retention in Heterogeneous Majority Dynamics.

A dynamics retains a specific information about the starting state of a networked multi-player system if this information can be computed from the state of the system also after several rounds of the dynamics. Information retention has been studied for the function that returns the majority of the states in systems in which players have states in ({0,1}) and the system evolves according to the majority dynamics: each player repeatedly updates its state to match the local majority among neighbors only. Positive and negative results have been given for probabilistic settings in which the initial states of the players are chosen at random and in worst-case settings in which the initial state is chosen non-deterministically.