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Geometric Tiles and Powers and Limitations of Geometric Hindrance in Self-assembly

  • Daniel Hader
  • Matthew J. PatitzEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11493)

Abstract

Tile-based self-assembly systems are capable of universal computation and algorithmically-directed growth. Systems capable of such behavior typically make use of “glue cooperation” in which the glues on at least 2 sides of a tile must match and bind to those exposed on the perimeter of an assembly for that tile to attach. However, several models have been developed which utilize “weak cooperation”, where only a single glue needs to bind but other preventative forces (such as geometric, or steric, hindrance) provide additional selection for which tiles may attach, and where this allows for algorithmic behavior. In this paper we first work in a model where tiles are allowed to have geometric bumps and dents on their edges. We show how such tiles can simulate systems of square tiles with complex glue functions (using asymptotically optimal sizes of bumps and dents). We also show that with only weak cooperation via geometric hindrance, no system in any model can simulate even a class of tightly constrained, deterministic cooperative systems, further defining the boundary of what is possible using this tool.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Computer Science and Computer EngineeringUniversity of ArkansasFayettevilleUSA

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