A Cellular Automaton Approach for Efficient Computing on Surface Chemical Reaction Networks

A surface chemical reaction network (sCRN, Qian and Winfree in DNA Computing and Molecular Programming: 20th International Conference, DNA 20, Kyoto, Japan, September 22-26, 2014. Proceedings 20. Springer, 2014) is an emergent paradigm for molecular programming, in which a chemical molecule is placed at each site of a lattice, and each molecule may undergo either bi-molecular reactions associated with one of the nearest molecules or uni-molecular reactions autonomously. The lattice structure as well as the localized reactions between molecules facilitate an effective formalization of sCRNs in the framework of cellular automata. This formalism not only allows a systematic evaluation of the complexity of a sCRN, but also enables a formal approach to reduce the model's complexity for the sake of improving its effectiveness. To this end, this paper proposes a new sCRN model that has less complexity measured in terms of the numbers of both cell states and transition rules. Especially, universality of computations will be shown by implementing all asynchronous circuits, including the well-known full-adder, into the sCRN. The decreased complexity may enhance the feasibility of the proposed sCRN model for physical implementation.