Computational classification of cellular automata

Abstract

We discuss attempts at the classification of cellular automata, in particular with a view towards decidability. We will see that a large variety of properties relating to the short-term evolution of configurations are decidable in principle, but questions relating to the long-term evolution are typically undecidable. Even in the decidable case, computational hardness poses a major obstacle for the automatic analysis of cellular automata.

Keywords:

• cellular automata
• classification
• Wolfram classes
• decidability
• automaticity