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Whether expansivity implies topological transitivity for general cellular automata

Establish whether, for general one-dimensional reversible cellular automata over finite alphabets, expansivity implies topological transitivity.

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Background

Within the GCA setting, the paper proves that expansivity implies topological transitivity. The authors point out that this implication is not known in the broader setting of general cellular automata, i.e., without the group structure on the alphabet.

Clarifying whether every expansive reversible cellular automaton (not restricted to group alphabets) is necessarily topologically transitive would extend the paper’s implication beyond GCAs and settle a basic structural question in cellular automata dynamics.

References

For general CAs, to the best of our knowledge, this has not yet been established.

— Decidability and Characterization of Expansivity for Group Cellular Automata (2510.14568 - Castronuovo et al., 16 Oct 2025) in Section 4 (Expansivity on general groups), immediately before Theorem \ref{espimplicatrans}