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Tight Bounds for Active Self-Assembly Using an Insertion Primitive

par Hescott, Benjamin B.J.;Malchik, Caleb;Winslow, Andrew
Référence Algorithmica, 77, 2, page (537-554)
Publication Publié, 2017-02

Article révisé par les pairs

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Résumé :

We prove two limits on the behavior of a model of self-assembling particles introduced by Dabby and Chen (Proceedings of 24th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1526–1536, 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=2Θ(k3/2) in O(log 5 / 3(n)) expected time, and that this is optimal in both the number of monomer types and expected time.