Algorithmica

, Volume 77, Issue 2, pp 537–554 | Cite as

Tight Bounds for Active Self-Assembly Using an Insertion Primitive

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Abstract

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

Keywords

DNA computing Biocomputing Formal languages Polymers Context-free grammars 

Notes

Acknowledgments

The authors thank anonymous reviewers for comments that improved the readability and correctness of the paper.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Benjamin Hescott
    • 1
  • Caleb Malchik
    • 1
  • Andrew Winslow
    • 2
  1. 1.Department of Computer ScienceTufts UniversityMedfordUSA
  2. 2.Département d’InformatiqueUniversité Libre de Bruxelles (ULB)BrusselsBelgium

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