No Perfect Two-State Cellular Automata for Density Classification Exists

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Abstract
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.

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