Freezing Simulates Non-freezing Tile Automata
Freezing Simulates Non-freezing Tile Automata
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DOI：
10.1007/978-3-030-00030-1_10
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发表时间：
2018-10
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影响因子：
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通讯作者：
Cameron T. Chalk;Austin Luchsinger;Eric Martinez;R. Schweller;Andrew Winslow;Tim Wylie
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作者：
Cameron T. Chalk;Austin Luchsinger;Eric Martinez;R. Schweller;Andrew Winslow;Tim Wylie
自组装是一个过程，通过这个过程，一个系统的粒子随机排列和联合收割机，通过局部相互作用，形成更大的复杂结构。在这项工作中，我们融合了一个特别的研究推广的瓷砖组装（2-HandedorHierarchical瓷砖组装模型）与概念，如状态和状态转换的特征在于相邻状态的元胞自动机。这使得主动自组装的概念得以简化，并为我们提供了将不同的现有模型联系起来的机制。我们表明，这个模型，coinedTile自动机，是不变的freezingandnon-freezingtransition规则通过模拟定理表明，任何非冻结瓷砖自动机系统可以模拟的冻结。冻结瓦片自动机系统限制状态转换，使得每个瓦片仅可访问状态一次，即，瓦片可以仅经历有限数量的转变。我们推测，这一结果可以用来表明，信号传递瓦片组装模型也是不变的，通过一系列的模拟结果之间的模型和瓦片自动机模型。此外，我们推测，这个模型可以用来巩固几个经常研究的自组装模型，其中组件可能会分裂，如信号传递瓦片组装模型，负胶2-手瓦片组装模型，和尺寸依赖瓦片组装模型。最后，瓦片自动机模型可能被证明是有用的，在细胞自动机与自组装相结合的结果。
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-HandedorHierarchical 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, coinedTile Automata, is invariant with respect tofreezingandnon-freezingtransition 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 theSignal-passing Tile Assembly Modelis 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, thenegative-glue2-Handed Tile Assembly Model, and theSize-Dependent Tile Assembly Model. Lastly, the Tile Automata model may prove useful in combining results in cellular automata with self-assembly.