Lecture Notes in Computer Science Volume 2943, 2004, pp 126-144

Proofreading Tile Sets: Error Correction for Algorithmic Self-Assembly

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Abstract

For robust molecular implementation of tile-based algorithmic self-assembly, methods for reducing errors must be developed. Previous studies suggested that by control of physical conditions, such as temperature and the concentration of tiles, errors (ε) can be reduced to an arbitrarily low rate – but at the cost of reduced speed (r) for the self-assembly process. For tile sets directly implementing blocked cellular automata, it was shown that rβε 2 was optimal. Here, we show that an improved construction, which we refer to as proofreading tile sets, can in principle exploit the cooperativity of tile assembly reactions to dramatically improve the scaling behavior to rβε and better. This suggests that existing DNA-based molecular tile approaches may be improved to produce macroscopic algorithmic crystals with few errors. Generalizations and limitations of the proofreading tile set construction are discussed.

This revised version was published in November 2004 and replaces the previous preliminary version.