Existence of a general-purpose physical machine for molecule output

Investigate whether a general-purpose physical machine capable of outputting any buildable molecule exists; if such a machine exists, formalize a notion of Kolmogorov complexity for physical molecules, and if not, establish the implications for defining Kolmogorov complexity for physical molecules.

Background

The authors argue that Kolmogorov complexity pertains to descriptions and that, for physical molecules, no general-purpose machine is known that outputs any molecule rather than a description. This undermines the applicability of Kolmogorov complexity to physical molecules as opposed to their representations.

Determining the existence or impossibility of such a machine bears on the theoretical bridge between algorithmic complexity and physical object complexity.