Staged Self-Assembly and Polyomino Context-Free Grammars

1. Staged Self-Assembly andPolyomino Context-Free Grammars Andrew Winslow

2. Tile

3. Glues

4. Assembly

6. ×∞ ×∞ ×∞ ×∞ Tile set

7. Mixing

8. Bin

9. Reagents

10. Products

12. Size

14. Staged self-assembly

15. Three glue types for any shape!

16. n How to assemble n-tile stick?

21. n ≈n size for n-tile stick

23. n ≈log(n) size for n-tile stick

24. n ≈n ≈log(n)

26. Finding small systems is difficult. Study a simplified model.

28. Rule

29. Grammar

30. One dimension 6× ? ? ? ? ? ? n0.5× #glues2× Staged System Grammar E. D. Demaine, S. Eisenstat, M. Ishaque, A. Winslow, One-dimensional staged self-assembly, DNA 17, 2011.

31. ? ? ? ?

32. Grammar

33. Two dimensions log(n)× w/scaling ? ? ? ≈n× ? ? ? Grammar Staged System

35. … … at least ≈n at most ≈log(n)

36. … … at least ≈n at most ≈log(n)

37. … … at least ≈n at most ≈log(n)

38. Grammar Staged System DNA 17 log(n)× 6× n0.5× This work w/scaling n×

39. Grammars are small, staged systems are always smaller Grammar Staged System log(n)× n0.5× 6× w/scaling ≈n×

40. Thank you