使用随机搅动的简单形状的快速算法自组装
Fast algorithmic self-assembly of simple shapes using random agitation
摘要：
我们研究了自组装的nubot模型中不受控制的随机分子运动的功率。nubot模型是一个异步的非确定性细胞自动机，增加了刚体运动规则（推/拉，确定性和编程性地应用于特定单体）和随机搅动（非确定性地应用于每个单体和方向，始终具有相等的概率）。之前关于nubot模型的工作展示了如何快速构建简单的形状，如线条和正方形--在预期的时间内，这仅仅是它们大小的对数。这些结果至关重要地利用了可编程刚体运动规则：单个单体快速控制大型物体运动的能力，并且只能在程序员选择的时间和地点。然而，在工程分子系统中，分子运动在很大程度上是不受控制的，并且基本上是随机的。这就提出了一个问题，即在一个限制性更强、也许更容易证明的模型中，是否可以实现类似的结果。在这个模型中，不受控制的随机运动或搅动在整个自组装过程中发生，并且是刚体运动的唯一形式。我们表明，这确实是这样的情况下：我们给一个polylogarithmic的预期时间建设广场使用搅拌，和一个次线性的预期时间建设，以建立一条线。这样的结果是不可能在一个搅拌自由（和运动自由）设置，从而显示利用不受控制的随机运动的好处。
英文摘要：
We study the power of uncontrolled random molecular movement in the nubot model of self-assembly. The nubot model is an asynchronous nondeterministic cellular automaton augmented with rigid-body movement rules (push/pull, deterministically and programmatically applied to specific monomers) and random agitations (nondeterministically applied to every monomer and direction with equal probability all of the time). Previous work on the nubot model showed how to build simple shapes such as lines and squares quickly---in expected time that is merely logarithmic of their size. These results crucially make use of the programmable rigid-body movement rule: the ability for a single monomer to control the movement of a large objects quickly, and only at a time and place of the programmers' choosing. However, in engineered molecular systems, molecular motion is largely uncontrolled and fundamentally random. This raises the question of whether similar results can be achieved in a more restrictive, and perhaps easier to justify, model where uncontrolled random movements, or agitations, are happening throughout the self-assembly process and are the only form of rigid-body movement. We show that this is indeed the case: we give a polylogarithmic expected time construction for squares using agitation, and a sublinear expected time construction to build a line. Such results are impossible in an agitation-free (and movement-free) setting and thus show the benefits of exploiting uncontrolled random movement.
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