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arXiv · 0903.1857

Limitations of Self-Assembly at Temperature 1

David Doty·Matthew J Patitz·Scott M Summers
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Abstract

We prove that if a set $X \subseteq \Z^2$ weakly self-assembles at temperature 1 in a deterministic tile assembly system satisfying a natural condition known as \emph{pumpability}, then $X$ is a finite union of semi-doubly periodic sets. This shows that only the most simple of infinite shapes and patterns can be constructed using pumpable temperature 1 tile assembly systems, and gives evidence for the thesis that temperature 2 or higher is required to carry out general-purpose computation in a tile assembly system. Finally, we show that general-purpose computation \emph{is} possible at temperature 1 if negative glue strengths are allowed in the tile assembly model.

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David Doty, Matthew J Patitz, Scott M Summers. 2009-03-10. Limitations of Self-Assembly at Temperature 1. https://arxiv.org/abs/0903.1857

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