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  • A systematic study of self-assembly as a mathematical process has been initiated by L. Adleman and E. Winfree. The individual components are modeled as square tiles on the infinite two-dimensional plane. In this paper we focus on a special type of structure, called a ribbon: a non-self-crossing rectilinear semence of tiles on the plane, in which successive tiles are adjacent along an edge and abutting edges of consecutive tiles have matching glues. We prove that it is undecidable whether an arbitrary finite set of tiles with glues (infinite supply of each tile type available) can be used to assemble an infinite ribbon. Our result settles an open problem formerly known as the “unlimited infinite snake problem.”
  • A systematic study of self-assembly as a mathematical process has been initiated by L. Adleman and E. Winfree. The individual components are modeled as square tiles on the infinite two-dimensional plane. In this paper we focus on a special type of structure, called a ribbon: a non-self-crossing rectilinear semence of tiles on the plane, in which successive tiles are adjacent along an edge and abutting edges of consecutive tiles have matching glues. We prove that it is undecidable whether an arbitrary finite set of tiles with glues (infinite supply of each tile type available) can be used to assemble an infinite ribbon. Our result settles an open problem formerly known as the “unlimited infinite snake problem.” (en)
Title
  • The undecidability of the infinite ribbon problem: implications for computing by self-assembly
  • The undecidability of the infinite ribbon problem: implications for computing by self-assembly (en)
skos:prefLabel
  • The undecidability of the infinite ribbon problem: implications for computing by self-assembly
  • The undecidability of the infinite ribbon problem: implications for computing by self-assembly (en)
skos:notation
  • RIV/47813059:19240/09:#0002978!RIV10-GA0-19240___
http://linked.open...avai/riv/aktivita
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  • P(GA201/06/0567)
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  • 6
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  • 347568
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  • RIV/47813059:19240/09:#0002978
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  • self-assembly; infinite snake problem; undecidability (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [E84831EEC06E]
http://linked.open...i/riv/nazevZdroje
  • SIAM J. on Computing
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http://linked.open...vavai/riv/projekt
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http://linked.open...v/svazekPeriodika
  • 38
http://linked.open...iv/tvurceVysledku
  • Sosík, Petr
  • Kari, Lila
issn
  • 0097-5397
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http://localhost/t...ganizacniJednotka
  • 19240
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