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

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

2009-06-17

arxiv.org/abs/0906.3251v1

EPTCS 1, 2009, pp. 67-69

Computer Science

Computational Complexity

Scientific paper

10.4204/EPTCS.1.6

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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