  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.

Computational Complexity