Size-Separable Tile Self-Assembly: A Tight Bound for Temperature-1 Mismatch-Free Systems

TL;DR

This paper introduces size-separability in tile self-assembly systems, demonstrating how to transform mismatch-free temperature-1 systems into size-separable ones with optimal parameters, facilitating practical filtering of assemblies.

Contribution

It proves that any mismatch-free temperature-1 system can be converted into a size-separable system with the same shape, achieving optimal scale and temperature.

Findings

Size-separable systems enable efficient filtering of assemblies.

Optimal scale factor and temperature are achieved in the transformation.

Independent results on mismatch-free temperature-1 two-handed systems are obtained.

Abstract

We introduce a new property of tile self-assembly systems that we call size-separability. A system is size-separable if every terminal assembly is a constant factor larger than any intermediate assembly. Size-separability is motivated by the practical problem of filtering completed assemblies from a variety of incomplete "garbage" assemblies using gel electrophoresis or other mass-based filtering techniques. Here we prove that any system without cooperative bonding assembling a unique mismatch-free terminal assembly can be used to construct a size-separable system uniquely assembling the same shape. The proof achieves optimal scale factor and temperature for the size-separable system. As part of the proof, we obtain two results of independent interest on mismatch-free temperature-1 two-handed systems.