Hypergraph Automata: A Theoretical Model for Patterned Self-assembly

TL;DR

This paper introduces self-assembly hypergraph automata as a new theoretical model for patterned self-assembly, demonstrating their computational equivalence to Wang Tile Systems without requiring predefined scanning strategies.

Contribution

It proposes SA-hypergraph automata as a novel automata-theoretic framework for patterned self-assembly, establishing their expressive power and advantages over existing models.

Findings

SA-hypergraph automata recognize all recognizable picture languages.

They are computationally equivalent to Wang Tile Systems.

They operate without a predefined scanning strategy.

Abstract

Patterned self-assembly is a process whereby coloured tiles self-assemble to build a rectangular coloured pattern. We propose self-assembly (SA) hypergraph automata as an automata-theoretic model for patterned self-assembly. We investigate the computational power of SA-hypergraph automata and show that for every recognizable picture language, there exists an SA-hypergraph automaton that accepts this language. Conversely, we prove that for any restricted SA-hypergraph automaton, there exists a Wang Tile System, a model for recognizable picture languages, that accepts the same language. The advantage of SA-hypergraph automata over Wang automata, acceptors for the class of recognizable picture languages, is that they do not rely on an a priori defined scanning strategy