Reverse-Robust Computation with Chemical Reaction Networks

TL;DR

This paper introduces a reverse-robust computation model for chemical reaction networks (CRNs), demonstrating that all semilinear predicates and functions can be computed reliably despite reversibility constraints.

Contribution

It extends the computational capabilities of CRNs to the reverse-robust model, showing existing constructions remain valid under reversibility limitations.

Findings

All semilinear predicates can be computed reverse-robustly.

Existing CRN constructions are valid under the reverse-robust model.

Invariants are key tools for ensuring correctness in reverse-robust CRNs.

Abstract

Chemical reaction networks, or CRNs, are known to stably compute semilinear Boolean-valued predicates and functions, provided that all reactions are irreversible. However, this property does not hold for wet-lab implementations, as all chemical reactions are reversible, even at very slow rates. We study the computational power of CRNs under the reverse-robust computation model, where reactions are permitted to occur either in forward or in reverse up to a cutoff point, after which they may only occur in forward. Our main results show that all semilinear predicates and all semilinear functions can be computed reverse-robustly, and in fact, that existing constructions continue to hold under the reverse-robust computational model. A key tool used to prove correctness under the reverse-robust computation model is invariants: linear (or linear modulo some $m$) combinations of the counts of the species that are preserved by all reactions.