The Tile Automata (TA) model describes self-assembly systems in which monomers can build structures and transition with an adjacent monomer to change their states. This paper shows that seeded TA is a non-committal intrinsically universal model of self-assembly. We present a single universal Tile Automata system containing approximately 4600 states that can simulate (a) the output assemblies created by any other Tile Automata system G, (b) the dynamics involved in building G's assemblies, and (c) G's internal state transitions. It does so in a non-committal way: it preserves the full non-deterministic dynamics of a tile's potential attachment or transition by selecting its state in a single step, considering all possible outcomes until the moment of selection. The system uses supertiles, each encoding the complete system being simulated. The universal system builds supertiles from its seed, each representing a single tile in G, transferring the information to simulate G to each new tile. Supertiles may also asynchronously transition states according to the rules of G. This result directly transfers to a restricted version of asynchronous Cellular Automata: pairwise Cellular Automata.
翻译:瓦片自动机(TA)模型描述了单体能够构建结构,并可通过与相邻单体发生状态转换的自组装系统。本文证明,种子化TA是一种非承诺性的内在普适自组装模型。我们提出了一种包含约4600个状态的单一通用瓦片自动机系统,该系统能够模拟(a)任何其他瓦片自动机系统G所生成的输出组装体,(b)构建G的组装体所涉及的动力学过程,以及(c)G的内部状态转换。其模拟以非承诺性方式实现:它通过单步选择瓦片状态,保留了瓦片潜在附着或转换的完全非确定性动力学,直至选择时刻前均考虑所有可能结果。该系统使用超瓦片,每片超瓦片编码了被模拟的完整系统。该通用系统从其种子开始构建超瓦片,每片超瓦片代表G中的一个瓦片,并将模拟G所需的信息传递给每个新瓦片。超瓦片还可根据G的规则异步转换状态。此结果可直接推广到异步细胞自动机的一个受限版本:成对细胞自动机。