# Output-Oblivious Stochastic Chemical Reaction Networks

## TL;DR

This paper characterizes which semilinear functions of two variables can be stably computed by output-oblivious stochastic chemical reaction networks, focusing on functions that are increasing and have specific structural properties.

## Contribution

It provides a complete classification of semilinear functions computable by output-oblivious CRNs with a leader, identifying conditions like being increasing and either grid-affine or a minimum of fissure functions.

## Key findings

- Characterizes output-oblivious CRN computability for semilinear functions.
- Shows that such functions must be increasing and have specific structural forms.
- Provides necessary and sufficient conditions for stable computation in this setting.

## Abstract

We classify the functions $f:\mathbb{N}^2 \rightarrow \mathbb{N}$ which are stably computable by output-oblivious Stochastic Chemical Reaction Networks (CRNs), i.e., systems of reactions in which output species are never reactants. While it is known that precisely the semilinear functions are stably computable by CRNs, such CRNs sometimes rely on initially producing too many output species and then consuming the excess in order to reach a correct stable state. These CRNs may be difficult to integrate into larger systems: if the output of a CRN $\mathcal{C}$ becomes the input to a downstream CRN $\mathcal{C}'$, then $\mathcal{C}'$ could inadvertently consume too many outputs before $\mathcal{C}$ stabilizes. If, on the other hand, $\mathcal{C}$ is output-oblivious then $\mathcal{C}'$ may consume $\mathcal{C}$'s output as soon as it is available. In this work we prove that a semilinear function $f:\mathbb{N}^2 \rightarrow \mathbb{N}$ is stably computable by an output-oblivious CRN with a leader if and only if it is both increasing and either grid-affine (intuitively, its domains are congruence classes), or the minimum of a finite set of fissure functions (intuitively, functions behaving like the min function).