Limitations of Self-Assembly at Temperature One (extended abstract)

David Doty; Matthew J. Patitz; Scott M. Summers

doi:10.4204/eptcs.1.6

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arXiv · 0906.3251

Limitations of Self-Assembly at Temperature One (extended abstract)

David Doty·Matthew J. Patitz·Scott M. Summers

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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.

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David Doty, Matthew J. Patitz, Scott M. Summers. 2009-06-17. Limitations of Self-Assembly at Temperature One (extended abstract). https://doi.org/10.4204/eptcs.1.6

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