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Randomized Self-Assembly for Exact Shapes

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1 Author(s)
Doty, D. ; Dept. of Comput. Sci., Iowa State Univ., Ames, IA, USA

Working in Winfree's abstract tile assembly model, we show that a constant-size tile assembly system can be programmed through relative tile concentrations to build an n × n square with high probability, for any sufficiently large n. This answers an open question of Kao and Schweller (Randomized Self-Assembly for Approximate Shapes, ICALP 2008), who showed how to build an approximately n×n square using tile concentration programming, and asked whether the approximation could be made exact with high probability.

Published in:

Foundations of Computer Science, 2009. FOCS '09. 50th Annual IEEE Symposium on

Date of Conference:

25-27 Oct. 2009