Document Type
Article
Publication Date
9-2023
Abstract
We analyze the complexity of two fundamental verification problems within a generalization of the two-handed tile self-assembly model (2HAM) where initial system assemblies are not restricted to be singleton tiles, but may be larger prebuilt assemblies. Within this model we consider the producibility problem, which asks if a given tile system builds, or produces, a given assembly, and the unique assembly verification (UAV) problem, which asks if a given system uniquely produces a given assembly. We show that producibility is NP-complete and UAV is coNPNP -complete even when the initial assembly size and temperature threshold are both bounded by a constant. This is in stark contrast to results in the standard model with singleton input tiles where producibility is in P and UAV is coNP-complete with constant temperature. We further provide preliminary polynomial time results for producibility and UAV in the case of 1-dimensional linear assemblies with pre-built assemblies, as well as extend our results to the abstract Tile Assembly Model (aTAM) with constant-size attachable assemblies.
Recommended Citation
Caballero, David, Timothy Gomez, Robert Schweller, and Tim Wylie. "Complexity of verification in self-assembly with prebuilt assemblies." Journal of Computer and System Sciences 136 (2023): 1-16. https://doi.org/10.1016/j.jcss.2023.03.002
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Publication Title
Journal of Computer and System Sciences
DOI
https://doi.org/10.1016/j.jcss.2023.03.002
Comments
Original published version available at https://doi.org/10.1016/j.jcss.2023.03.002