Identifying shapes using self-assembly

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. © 2010 Springer-Verlag.