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Determine global universality of Rule 110

Determine whether the elementary cellular automaton Rule 110 is globally universal, i.e., whether it can simulate any one-dimensional cellular automaton via local, translation-invariant encodings and decodings as defined by the paper’s global simulation framework.

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Background

The authors show Rule 110 is locally universal with polynomial encoder/decoder complexity and discuss that global universality is strictly stronger than local universality. They emphasize that global universality would imply universal self-replication via their 1D von Neumann-style construction.

They state that, despite local universality proofs, global universality of Rule 110 would require a different encoding than known constructions and remains unresolved.

References

It would suffice for Rule 110 to be globally universal (as this would imply universal self-replication on account of our d = 1 version of von Neumann's construction), but this is not known.

— Self-replication and Computational Universality (2510.08342 - Cotler et al., 9 Oct 2025) in Section 'Open problems and conjectures' (Turning to specific CAs)