Limitations of Self-Assembly at Temperature One (extended abstract)
Computational Complexity
2009-06-18 v1
Abstract
We prove that if a subset X of the integer Cartesian plane weakly self-assembles at temperature 1 in a deterministic (Winfree) tile assembly system satisfying a natural condition known as *pumpability*, then X is a finite union of 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 strong 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 is possible at temperature 1 if negative glue strengths are allowed in the tile assembly model.
Keywords
Cite
@article{arxiv.0906.3251,
title = {Limitations of Self-Assembly at Temperature One (extended abstract)},
author = {David Doty and Matthew J. Patitz and Scott M. Summers},
journal= {arXiv preprint arXiv:0906.3251},
year = {2009}
}