staged self-assembly and polyomino context-free grammars
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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Staged Self-Assembly andPolyomino Context-Free
GrammarsAndrew Winslow
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Tile
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Glues
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Assembly
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×∞ ×∞ ×∞ ×∞Tile set
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Mixing
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Bin
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Reagents
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Products
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Size
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Staged self-assembly
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Three glue types for any shape!
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How to assemble n-tile stick?
n
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n≈n size for n-tile stick
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n ≈log(n) size for n-tile stick
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n
≈n ≈log(n)
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Study a simplified model.
Finding small systems is difficult.
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Rule
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Grammar
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#glues2×
Staged System
? ? ?
One dimension
6×
n0.5×
E. D. Demaine, S. Eisenstat, M. Ishaque, A. Winslow, One-dimensional staged self-assembly, DNA 17, 2011.
Grammar
? ? ?
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? ? ? ?
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Grammar
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Two dimensions
Grammar Staged System
≈n×
log(n)×
? ? ?? ? ?w/scaling
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at most ≈log(n)
…
at least ≈n
…
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at most ≈log(n)
…
at least ≈n
…
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at most ≈log(n)
…
at least ≈n
…
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Grammar Staged System
log(n)×
n×
6×
n0.5×
w/scalingThis work
DNA 17
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Grammar Staged System
log(n)×
≈n×
6×
n0.5×
w/scaling
Grammars are small,staged systems are always
smaller
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Thank you