基于插入基元的主动自组装的紧边界
Tight Bounds for Active Self-Assembly Using an Insertion Primitive
摘要：
我们证明了两个紧边界的行为的自组装粒子的模型介绍了达比和陈（SODA 2013），称为插入系统，其中单体插入到一个不断增长的线性聚合物的中间。首先，我们证明了这些系统的表达能力等于上下文无关文法，回答了一个问题提出的达比和陈。其次，我们证明了系统的$k$单体类型可以确定性地构建聚合物的长度$n = 2^{Θ(k^{3/2})}$在$O(\log^{5/3}(n))$预期的时间，这是最佳的单体类型和预期的时间。
英文摘要：
We prove two tight bounds on the behavior of a model of self-assembling particles introduced by Dabby and Chen (SODA 2013), called insertion systems, where monomers insert themselves into the middle of a growing linear polymer. First, we prove that the expressive power of these systems is equal to context-free grammars, answering a question posed by Dabby and Chen. Second, we prove that systems of $k$ monomer types can deterministically construct polymers of length $n = 2^{Θ(k^{3/2})}$ in $O(\log^{5/3}(n))$ expected time, and that this is optimal in both the number of monomer types and expected time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
