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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.

Randomized Self-Assembly for Exact Shapes