Hypergraph Automata: A Theoretical Model for Patterned Self-assembly
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
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Cite
@article{arxiv.1302.2840,
title = {Hypergraph Automata: A Theoretical Model for Patterned Self-assembly},
author = {Lila Kari and Steffen Kopecki and Amirhossein Simjour},
journal= {arXiv preprint arXiv:1302.2840},
year = {2013}
}
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25 pages