Simple example CRNs from lecture that stably compute functions have the property that they have bounded executions (the number of reactions on any given input cannot be infinite). But the general technique to compute any semilinear function allows arbitrarily long executions. Is this necessary, or can all semilinear functions be computed with CRNs that have bounded executions? (Note: This may have been solved by someone in a project in another course, but I'm not sure it was ever published.)
All chemical reactions are reversible, even at some very slow rate. If a CRN is reversible (meaning all of its reactions are reversible), then it cannot have stable configurations, since the last reaction to make the configuration "stable" could always be reversed (hence it cannot really be a stable configuration). Can we design CRNs that compute functions that are "reverse-robust" in the sense that, for any configuration reachable from the initial configuration by either forward or reverse reactions, there is a configuration reachable by only forward reactions that is correct and stable? (where stable is also defined only with respect to forward reactions)
The paper The Power of Nondeterminism in Self-Assembly shows that there is an infinite shape S such that some TAS strictly self-assembles S, but no directed TAS strictly self-assembles S. It crucially uses the fact that if a single strength-τ glue connects a tile to the rest of the assembly, then there is no way to guarantee that the tile is attached before some other attachments happen. It could always be the case that arbitrarily many other attachments happen first. However, much of the interesting behavior possible in the temperature-2 aTAM using strength-2 glues can be had using "duples" (https://arxiv.org/abs/1402.4515) and only strength-1 glues. However, it is not clear how to apply the duple "technology" to the constructions of the paper. It is open whether a similar result can be proved in a TAS that allows duples and forbids strength-τ glues.
Authors of papers I did list have several other papers in the field; check their webpages.