Editing Open Problems (section)

=== Problem context ===

Chemical reaction networks are known to be Turing-universal with probability $1-\epsilon$ (for any $\epsilon>0$) [<ref name="SCWB2008">Soloveichik, D., Cook, M., Winfree, E., & Bruck, J. (2008). Computation with finite stochastic chemical reaction networks. Natural Computing, 7(4), 615-633.</ref>.] CRNs augmented with a constant number of ''stacks'' are Turing-universal <ref name="QSW2011">Qian, L., Soloveichik, D., & Winfree, E. (2011).  Efficient Turing-universal computation with DNA polymers. In DNA computing and molecular programming (pp. 123-140). Springer Berlin Heidelberg.</ref>.   This was demonstrated using a DNA strand displacement system construction that exploited the fact that DNA can easily form ''polymers''.  The stacks in that construction behave as one would expect: a molecule can be added to the top of the stack, can be removed from the top of the stack, and molecules not on the top are not accessible to other reactions. A stack of type $i$ initiates from a special subunit molecule called $\bot_i$. Simplifying details from <ref name="QSW2011" />, this leads to CRN reactions of the form:

$$
\begin{align}
  [\bot_i \ldots X] + Y &\rightarrow [\bot_i \ldots XY]\\
  [\bot_i \ldots XY] + POP_i &\rightarrow [\bot_i \ldots X] + Y
\end{align}
$$

==== Initial context assumption ====

As with many results that demonstrate CRNs capable of complex computation <ref name="SCWB2008" /><ref name="TC2012">Thachuk, C., & Condon, A. (2012). Space and energy efficient computation with DNA strand displacement systems. In DNA Computing and Molecular Programming (pp. 135-149). Springer Berlin Heidelberg.</ref>, the stack machine construction in <ref name="QSW2011" /> assumes that certain molecular species are present in exact initial quantities, in particular there is exactly one copy of each stack.