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Reachability complexity in restricted CRN variants

Determine the computational complexity of the reachability problem for restricted instances of the CRN variants studied in the paper, including deletion-only versions and other constrained subclasses of Inhibitory CRNs, Coarse-Rate CRNs, Step-Cycle CRNs, Unique-Instruction Parallel CRNs, and Void Genesis CRNs.

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Background

Reachability in Petri nets/VASS is known to be of extremely high complexity, and the paper references recent results as well as specific findings for step-cycles and deletion-only settings.

The authors highlight that while some step-cycle results are known, deletion-only rules and other restricted variants have not been fully explored for the other CRN models considered, posing a concrete direction to classify their reachability complexity.

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}): What is the complexity of reachability in restricted instances of each model, such as ? As mentioned, we know the complexity with step-cycles , but deletion-only rules have not been explored in detail in the other models.

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