1. Staged Self-Assembly and Polyomino 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. How to assemble n-tile stick?

21. ≈n size for n-tile stick

23. ≈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 ? ? ? ? ? ? Grammar Staged System 6× #glues2× n0.5×
? ? ?
Grammar
? ? ? 6×
n0.5×
#glues2×
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 most ≈log(n) …
at least ≈n …

36. … …
at least ≈n
at most ≈log(n)

37. … …
at least ≈n
at most ≈log(n)

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

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

40. Thank you