Applying Symmetric Enumeration Method to One-Dimensional Assembly of Rotatable Tiles

  • Satoshi KobayashiEmail author
Part of the Natural Computing Series book series (NCS)


Motivated by the increasing importance of the analysis of a complicated reaction system where molecules are interacting in various ways to produce a huge number of compounds of molecules, the author’s previous work proposed a new approach, called Symmetric Enumeration Method (SEM), to the efficient analysis of such reaction systems. The proposed theory provided a general method for the efficient computation of equilibrium states. In this paper, we will review the results of the theory of SEM, and apply it to the equilibria analysis of a one-dimensional assembly system of tiles which can be rotated around three axes, i.e., the x-, y-, and z-axes. Although the growth of a tile assembly is restricted to only one-dimensional direction, the exhaustive method of generating all tile assemblies and obtaining equilibria is intractable since the number of assemblies could be exponential with respect to the number of tiles given to the system. We will show that this equilibria analysis can be transformed into a convex programming problem with a set of variables of size polynomial with respect to the number of input tiles.


Assembly System Enumeration Scheme Free Energy Function Graph Component Convex Programming Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of Electro-CommunicationsTokyoJapan

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