A Formal Model of Universal Algorithmic Assembly and Molecular Computation

In this paper, the author describes a systematic and general approach to nanostructure synthesis and control through autonomous molecular combinatory computing. Combinatory computing is based on simple network (graph) substitution operations, deriving from combinatory logic (Curry, Feys, & Craig, 1958), which are sufficient for any computation. When these operations are implemented by autonomous molecular processes, they provide a means for computing within supramolecular networks, which may be used to assemble these networks or control their behavior. Further, the Church-Rosser Theorem (Curry, Feys, & Craig, 1958) proves that substitutions may be performed in any order or in parallel without affecting the computational result; this is a very advantageous property for autonomous molecular computation. In addition to the theoretical foundations of molecular combinatory computing, the author discusses possible molecular implementations as well as accomplishments in the (simulated) synthesis of membranes, channels, nanotubes, and other nanostructures.