Exact results for one-dimensional cellular automata with different types of updates

This work derives explicit relations between the densities and correlation functions for these different stationary states for one-dimensional stochastic cellular automata with arbitrary nearest-neighbor interactions and arbitrary open boundary conditions.

Abstract

We study two common types of time-noncontinuous updates for one dimensional\nstochastic cellular automata with arbitrary nearest neighbor interactions and\narbitrary open boundary conditions. We first construct the stationary states\nusing the matrix product formalism. This construction then allows to prove a\ngeneral connection between the stationary states which are produced by the two\ndifferent types of updates. Using this connection, we derive explicit relations\nbetween the densities and correlation functions for these different stationary\nstates.\n