Tight Bounds for Active Self-Assembly Using an Insertion Primitive

Benjamin Hescott; Caleb Malchik; Andrew Winslow

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arXiv · 1401.0359

Tight Bounds for Active Self-Assembly Using an Insertion Primitive

Benjamin Hescott·Caleb Malchik·Andrew Winslow

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Abstract

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 $n = 2^{\Theta(k^{3/2})}$ in $O(\log^{5/3}(n))$ expected time, and that this is optimal in both the number of monomer types and expected time.

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Benjamin Hescott, Caleb Malchik, Andrew Winslow. 2014-01-02. Tight Bounds for Active Self-Assembly Using an Insertion Primitive. https://arxiv.org/abs/1401.0359

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