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Relationship between Coarse-Rate CRNs and k-rate CRNs

Determine the formal relationship between Coarse-Rate chemical reaction networks with two reaction ranks and generalized k-rate chemical reaction networks that allow k distinct reaction ranks, under the paper's notion of polynomial efficient simulation or another appropriate equivalence.

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Background

The paper studies Coarse-Rate CRNs where reactions are partitioned into two ranks (fast vs. slow) and establishes polynomial simulation equivalence among several CRN variants using the Void Genesis model as a hub.

A natural generalization is to allow more than two ranks. Understanding how 2-rank Coarse-Rate CRNs relate to k-rate CRNs (k ≥ 3) would extend the equivalence landscape and clarify whether additional ranks increase expressive or simulation power beyond polynomial overhead.

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}): Coarse-Rate CRNs are limited to 2 ranks for reactions. A natural generalization of this model is to allow for $k$ different ranks ($k$-rate CRNs). What is the relationship between Coarse-Rate CRNs and $k$-rate CRNs?

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