Tight bounds for active self-assembly using an insertion primitive

Abstract

We prove two tight bounds on the behavior of a model of self-assembling particles introduced by Dabby and Chen (SODA 2012), 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 polymers of length 2θ(k3/2)can be deterministically constructed by insertion systems of k monomer types in O((logn)5/3) expected time, and that this is the best possible in both the number of types and expected time. © 2014 Springer-Verlag Berlin Heidelberg.