No Perfect Two-State Cellular Automata for Density Classification Exists
Mark Land, Richard K. Belew · Physical Review Letters · 1995
Recently there have been many attempts to evolve one-dimensional two-state cellular automata which classify binary strings according to their densities of 1's and 0's. The current best-known approaches involve particle-based systems of information transfer. A proof is given that there does not exist a two-state cellular automata which performs the task perfectly. This is true even in multiple dimensions.