Identifying Shapes Using Self-Assembly (extended abstract)

TL;DR

This paper explores the computational complexity of designing tile-based self-assembly systems that can uniquely identify whether an input shape matches a target shape, focusing on squares and more general hole-free shapes.

Contribution

It introduces a new problem in algorithmic self-assembly for shape identification and analyzes its complexity for various shape classes.

Findings

Complexity results for square shape identification

Complexity analysis for general hole-free shapes

Insights into the design of self-assembly systems for shape recognition

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.