种子活动瓦片自组装中的内在普遍性
Intrinsic Universality in Seeded Active Tile Self-Assembly
AI总结：
本文提出一个包含约4600状态的通用瓦片自动机系统，以非承诺方式模拟任何其他种子型瓦片自动机系统的组装、动力学和状态转换，并适用于成对元胞自动机。
摘要：
瓦片自动机（Tile Automata, TA）模型描述了这样的自组装系统：单体可以构建结构，并与相邻单体发生状态转换以改变自身状态。本文证明，种子型TA是一种非承诺性的内在普遍自组装模型。我们提出了一个包含约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所产生的输出组装结构，（b）构建G的组装结构所涉及的动力学过程，以及（c）G的内部状态转换。它以一种非承诺性的方式实现这一点：通过单步选择其状态，保留瓦片潜在附着或转换的完整非确定性动力学，在选择的时刻之前考虑所有可能的结果。该系统使用超级瓦片，每个超级瓦片编码被模拟的完整系统。通用系统从其种子构建超级瓦片，每个超级瓦片代表G中的一个单个瓦片，并将模拟G的信息传递给每个新瓦片。超级瓦片也可以根据G的规则异步转换状态。这一结果直接适用于异步元胞自动机的一种受限版本：成对元胞自动机。
英文摘要：
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.
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