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Freezing Simulates Non-freezing Tile Automata

  • Cameron Chalk
  • Austin Luchsinger
  • Eric Martinez
  • Robert Schweller
  • Andrew Winslow
  • Tim WylieEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11145)

Abstract

Self-assembly is the process by which a system of particles randomly agitate and combine, through local interactions, to form larger complex structures. In this work, we fuse a particular well-studied generalization of tile assembly (the 2-Handed or Hierarchical Tile Assembly Model) with concepts from cellular automata such as states and state transitions characterized by neighboring states. This allows for a simplification of the concepts from active self-assembly, and gives us machinery to relate the disparate existing models. We show that this model, coined Tile Automata, is invariant with respect to freezing and non-freezing transition rules via a simulation theorem showing that any non-freezing tile automata system can be simulated by a freezing one. Freezing tile automata systems restrict state transitions such that each tile may visit a state only once, i.e., a tile may undergo only a finite number of transitions. We conjecture that this result can be used to show that the Signal-passing Tile Assembly Model is also invariant to this constraint via a series of simulation results between that model and the Tile Automata model. Further, we conjecture that this model can be used to consolidate the several oft-studied models of self-assembly wherein assemblies may break apart, such as the Signal-passing Tile Assembly Model, the negative-glue 2-Handed Tile Assembly Model, and the Size-Dependent Tile Assembly Model. Lastly, the Tile Automata model may prove useful in combining results in cellular automata with self-assembly.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Cameron Chalk
    • 1
  • Austin Luchsinger
    • 2
  • Eric Martinez
    • 2
  • Robert Schweller
    • 2
  • Andrew Winslow
    • 2
  • Tim Wylie
    • 2
    Email author
  1. 1.Department of Electrical and Computer EngineeringUniversity of Texas at AustinAustinUSA
  2. 2.Department of Computer ScienceUniversity of Texas Rio Grande ValleyEdinburgUSA

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