The tile assembly model is intrinsically universal

TL;DR

This paper proves that the abstract Tile Assembly Model (aTAM) is intrinsically universal, demonstrating a single tile system that can simulate any other aTAM system through a biologically inspired, asynchronous decision-making process.

Contribution

It introduces a universal tile assembly system that can simulate any aTAM system at any temperature, using a novel genome-based decision process for self-assembly.

Findings

Universal tile assembly system constructed for all aTAM models

Simulation preserves deterministic and nondeterministic behaviors

Works at any temperature in the aTAM

Abstract

We prove that the abstract Tile Assembly Model (aTAM) of nanoscale self-assembly is intrinsically universal. This means that there is a single tile assembly system U that, with proper initialization, simulates any tile assembly system T. The simulation is "intrinsic" in the sense that the self-assembly process carried out by U is exactly that carried out by T, with each tile of T represented by an m x m "supertile" of U. Our construction works for the full aTAM at any temperature, and it faithfully simulates the deterministic or nondeterministic behavior of each T. Our construction succeeds by solving an analog of the cell differentiation problem in developmental biology: Each supertile of U, starting with those in the seed assembly, carries the "genome" of the simulated system T. At each location of a potential supertile in the self-assembly of U, a decision is made whether and how to express this genome, i.e., whether to generate a supertile and, if so, which tile of T it will represent. This decision must be achieved using asynchronous communication under incomplete information, but it achieves the correct global outcome(s).