Difference between revisions of "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. | |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. | ||
|authors=Matthew J. Patitz and Scott M. Summers | |authors=Matthew J. Patitz and Scott M. Summers | ||
|file=[http://arxiv.org/abs/1006.3046 Arxiv page] | |file=[http://arxiv.org/abs/1006.3046 Arxiv page] | ||
}} | }} | ||
Revision as of 21:47, 29 November 2011
Published on:
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.
Authors
Matthew J. Patitz and Scott M. Summers
