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arXiv · 1404.7410

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

Andrew Winslow
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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.

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Andrew Winslow. 2014-04-29. Size-Separable Tile Self-Assembly: A Tight Bound for Temperature-1 Mismatch-Free Systems. https://arxiv.org/abs/1404.7410

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