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Turing universality of void Step-Cycle CRNs

Establish whether Step-Cycle chemical reaction networks restricted to void reactions (that is, rules that create no species) are Turing universal.

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Background

The paper shows polynomial simulation equivalence among several CRN variants and notes that step CRNs with only void reactions can compute threshold circuits, suggesting substantial computational power even under severe reaction constraints.

The authors ask whether the Step-Cycle extension under the same void-only restriction attains full Turing universality, which would strengthen the understanding of the minimal features needed for universal computation in CRN-like systems.

References

While this work is complete in proving equivalence between these models, there are still several interesting open problems to consider (some of which are shown in Figure \ref{fig:vg_hub}): Even when limited to only void reactions (rules where no species are created), step CRNs are able to compute threshold circuits . Does this suggest that Step-Cycle CRNs, even when limited to only void reactions (void Step-Cycle), are still Turing Universal?

— Polynomial Equivalence of Extended Chemical Reaction Models (2509.15584 - Bajaj et al., 19 Sep 2025) in Section 6 (Conclusion)