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Staged Self-Assembly and Polyomino Context-Free Grammars

Staged Self-Assembly and Polyomino Context-Free Grammars. Andrew Winslow. Tile. Glues. Assembly. ×∞. ×∞. ×∞. ×∞. Tile set. M ixing. Bin. Reagents. Products. Size. Staged self-assembly. Three glue types for any shape!. n. How to assemble n-tile stick? . n.

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Staged Self-Assembly and Polyomino Context-Free Grammars

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

  2. Tile

  3. Glues

  4. Assembly

  5. ×∞ ×∞ ×∞ ×∞ Tile set

  6. Mixing

  7. Bin

  8. Reagents

  9. Products

  10. Size

  11. Staged self-assembly

  12. Three glue types for any shape!

  13. n How to assemble n-tile stick?

  14. n ≈n size for n-tile stick

  15. n ≈log(n) size for n-tile stick

  16. n ≈n ≈log(n)

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

  18. Rule

  19. Grammar

  20. 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.

  21. ? ? ? ?

  22. Grammar

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

  24. … at least ≈n at most ≈log(n)

  25. … at least ≈n at most ≈log(n)

  26. … at least ≈n at most ≈log(n)

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

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

  29. Thank you

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