自组装系统是分布式系统
Self-Assembling Systems are Distributed Systems
摘要：
2004年，Klavins等人引入了使用图语法来描述和编程自组装系统。我们表明，这些图文法可以嵌入到一个图重写表征的分布式系统，提出了由Degano和Montanari超过二十年前。我们应用这种嵌入推广Soloveichik和Winfree的本地确定性标准（实现一个独特的终端组装），从组装系统的4边瓷砖，嵌入在平面上，任意图形组装系统。我们提出了一个部分逆的嵌入结果，通过提供充分的条件下，分布式处理器系统可以模拟图组装系统的拓扑，在平面上，并在3-空间。最后，我们定义了一个新的复杂性措施：“表面成本”（本质上是凸包的空间居住的代理在一个自组装计算的结论）。我们发现，对于增长有界图，执行一个子程序，找到一个最大的独立集只增加了表面成本的自组装计算的一个常数因子。我们得到这个复杂性的限制，通过使用模拟结果导入的分布式计算的概念，“本地同步器”和“确定性抛硬币”到自组装。
英文摘要：
In 2004, Klavins et al. introduced the use of graph grammars to describe -- and to program -- systems of self-assembly. We show that these graph grammars can be embedded in a graph rewriting characterization of distributed systems that was proposed by Degano and Montanari over twenty years ago. We apply this embedding to generalize Soloveichik and Winfree's local determinism criterion (for achieving a unique terminal assembly), from assembly systems of 4-sided tiles that embed in the plane, to arbitrary graph assembly systems. We present a partial converse of the embedding result, by providing sufficient conditions under which systems of distributed processors can be simulated by graph assembly systems topologically, in the plane, and in 3-space. We conclude by defining a new complexity measure: "surface cost" (essentially the convex hull of the space inhabited by agents at the conclusion of a self-assembled computation). We show that, for growth-bounded graphs, executing a subroutine to find a Maximum Independent Set only increases the surface cost of a self-assembling computation by a constant factor. We obtain this complexity bound by using the simulation results to import the distributed computing notions of "local synchronizer" and "deterministic coin flipping" into self-assembly.
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