Randomized Self-Assembly for Exact Shapes

— 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.

• Type: Conference
• Year: 2009
• Where: FOCS
• Authors: David Doty
• Keywords: FOCS 2009, Relative Tile Concentrations, Theoretical Computer Science, Tile Assembly, Tile Concentration