Reachability Problems for Continuous Chemical Reaction Networks

TL;DR

This paper studies the reachability problem in rate-independent continuous chemical reaction networks, showing polynomial-time algorithms for some cases and NP-completeness for related problems, advancing understanding of chemical computation models.

Contribution

It proves polynomial-time computability of reachability in CCRNs and NP-completeness of a related subproblem, clarifying computational complexity in this model.

Findings

Reachability in CCRNs is polynomial-time computable.

Sub-CCRN-REACH is NP-complete.

Advances understanding of computational complexity in chemical reaction networks.

Abstract

Chemical reaction networks (CRNs) model the behavior of molecules in a well-mixed system. The emerging field of molecular programming uses CRNs not only as a descriptive tool, but as a programming language for chemical computation. Recently, Chen, Doty and Soloveichik introduced a new model of chemical kinetics, rate-independent continuous CRNs (CCRNs), to study the chemical computation of continuous functions. A fundamental question of a CRN is whether a state of the system is reachable through a sequence of reactions in the network. This is known as the reachability problem. In this paper, we investigate CCRN-REACH, the reachability problem for this model of chemical reaction networks. We show that, for continuous CRNs, constructing a path to a state of the network is computable in polynomial time. We also prove that a related problem, Sub-CCRN-REACH, is NP-complete.