English

Hypergraph Automata: A Theoretical Model for Patterned Self-assembly

Discrete Mathematics 2013-02-13 v1 Formal Languages and Automata Theory Combinatorics

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

Keywords

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}
}

Comments

25 pages

R2 v1 2026-06-21T23:24:53.812Z