A Study on Complexity Measure of Diamond Tile Self-assembly System

  • M. Nithya Kalyani
  • P. Helen Chandra
  • S. M. Saroja T. Kalavathy
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 834)

Abstract

Molecular self-assembly gives rise to a great diversity of complex forms from crystals and DNA helices to microtubules and holoenzymes. We study a formal self-assembly model called the Diamond Tile Assembly System in which a diamond tile may be added to the growing object when the total interaction strength with its neighbours exceeds a parameter \(\mathcal {T}\). Self-assembled objects can also be studied from the point of view of computational complexity. Here, we define the program-size complexity of an \(N\,\times \,N\) diamond to be the minimum number of distinct tiles required to self-assemble the diamond. We study this complexity under the Diamond Tile Assembly Model and find a dramatic decrease in complexity from \(N^{2}\) tiles to O(logN) tiles, as \(\mathcal {T}\) is increased from 1 where bonding is non co-operative to 2 allowing co-operative bonding. Further, we observe that the size of the largest diamond uniquely produced by a set of n tiles grows faster than any computable function.

Keywords

Self-assembly Diamond Tile Assembly Program-size complexity 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Jayaraj Annapackiam College for Women (Autonomous)Periyakulam, Theni DistrictIndia

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