Document Type
Conference Proceeding
Publication Date
4-2022
Abstract
Tile Automata is a recently defined model of self-assembly that borrows many concepts from cellular automata to create active self-assembling systems where changes may be occurring within an assembly without requiring attachment. This model has been shown to be powerful, but many fundamental questions have yet to be explored. Here, we study the state complexity of assembling n × n squares in seeded Tile Automata systems where growth starts from a seed and tiles may attach one at a time, similar to the abstract Tile Assembly Model. We provide optimal bounds for three classes of seeded Tile Automata systems (all without detachment), which vary in the amount of complexity allowed in the transition rules. We show that, in general, seeded Tile Automata systems require Θ(log^{1/4} n) states. For Single-Transition systems, where only one state may change in a transition rule, we show a bound of Θ(log^{1/3} n), and for deterministic systems, where each pair of states may only have one associated transition rule, a bound of Θ(({log n}/{log log n})^{1/2}).
Recommended Citation
Alaniz, R. M., Caballero, D., Cirlos, S. C., Gomez, T., Grizzell, E., Rodriguez, A., ... & Wylie, T. (2022). Building Squares with Optimal State Complexity in Restricted Active Self-Assembly. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Schloss Dagstuhl-Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SAND.2022.6
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Title
1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)
DOI
10.4230/LIPIcs.SAND.2022.6
Comments
© Robert M. Alaniz, David Caballero, Sonya C. Cirlos, Timothy Gomez, Elise Grizzell, Andrew Rodriguez, Robert Schweller, Armando Tenorio, and Tim Wylie;