After the Adleman-Lipton [1] paradigm for DNA computation emerged, several methods to exploit the inherent large-scale coding abilities of polynucleotide strands were proposed [2]. The onus was on each model’s proponents to demonstrate its expressive computational power and universality. This paper is an interesting approach to formalizing molecular computations, but the proof presented to reach that goal is rather tedious.

Before debating the issues with the proof of the equivalence between the artificial chemistry proposed and a universal Turing machine, let’s examine the proposed formalism. Procedural operative processes are modeled using an artificial chemistry that captures information about reactant recombination for arbitrary sets of molecules (finite alphabets corresponding to molecular building blocks, for example, polynucleotide bases), limited to strings. It is thus possible to model the precise chain of reactant-induced recombination dynamics during a computational molecular procedure.

This artificial chemistry is formalized using string transformation rules and can thus be useful at various levels. This is demonstrated in the paper by applying it to the Adleman-Lipton procedure and a newer automaton-based paradigm. A proof of the universality and expressive power of the artificial chemistry shows that, for three-reactant recombination rules, the chemistry can represent a universal Turing machine, with the ability to mechanically transform such representation into one-reactant or two-reactant computation rules. However, the proofs presented are very clumsy, as is the notation system used. In many cases, contextual notation is used without introduction; this level of disorganization is not suitable for a well-defined formal system.

The comparison with other artificial chemistries is rather superficial and its differentiating features are only briefly noted. The strength of the formalism remains to be shown through concrete examples or proofs of complexity. Indeed, the added value of new artificial computation techniques lies more in their ability to reduce algorithmic complexity, rather than universality. This has long been established for well-formed rule-based chemistries through rewriting [2]. In this regard, the symbolic representation of the Adleman-Lipton mechanism is illustrative, but not demonstrative.