Identifying Shapes Using Self‐assembly

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.