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.
@article{arxiv.1006.3046,
title = {Identifying Shapes Using Self-Assembly (extended abstract)},
author = {Matthew J. Patitz and Scott M. Summers},
journal= {arXiv preprint arXiv:1006.3046},
year = {2010}
}