  Here we focus on the challenge of verifying the correctness of molecular
implementations of abstract chemical reaction networks, where operation in a
well-mixed "soup" of molecules is stochastic, asynchronous, concurrent, and
often involves multiple intermediate steps in the implementation, parallel
pathways, and side reactions. This problem relates to the verification of Petri
nets, but existing approaches are not sufficient for providing a single
guarantee covering an infinite set of possible initial states (molecule counts)
and an infinite state space potentially explored by the system given any
initial state. We address these issues by formulating a new theory of pathway
decomposition that provides an elegant formal basis for comparing chemical
reaction network implementations, and we present an algorithm that computes
this basis. Our theory naturally handles certain situations that commonly arise
in molecular implementations, such as what we call "delayed choice," that are
not easily accommodated by other approaches. We further show how pathway
decomposition can be combined with weak bisimulation to handle a wider class
that includes most currently known enzyme-free DNA implementation techniques.
We anticipate that our notion of logical equivalence between chemical reaction
network implementations will be valuable for other molecular implementations
such as biochemical enzyme systems, and perhaps even more broadly in
concurrency theory.
