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Identifying Shapes Using Self-assembly

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Abstract

In this paper, we introduce the following problem in the theory of algorithmic self-assembly: given an input shape as the seed of a tile-based self-assembly system, design a finite tile set that can, in some sense, uniquely identify whether or not the given input shape—drawn from a very general class of shapes—matches a particular target shape. We first study the complexity of correctly identifying squares. Then we investigate the complexity associated with the identification of a considerably more general class of non-square, hole-free shapes.

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Authors and Affiliations

  1. Department of Computer Science, University of Texas-Pan American, Edinburg, TX, 78539, USA

    Matthew J. Patitz

  2. Department of Computer Science and Software Engineering, University of Wisconsin-Platteville, Platteville, WI, 53818, USA

    Scott M. Summers

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  1. Matthew J. Patitz
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Correspondence to Scott M. Summers.

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Patitz, M.J., Summers, S.M. Identifying Shapes Using Self-assembly. Algorithmica 64, 481–510 (2012). https://doi.org/10.1007/s00453-011-9549-7

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