Date of Graduation
5-2018
Document Type
Thesis
Degree Name
Bachelor of Science in Computer Engineering
Degree Level
Undergraduate
Department
Computer Science and Computer Engineering
Advisor/Mentor
Patitz, Matthew
Committee Member/Reader
Andrews, David
Committee Member/Second Reader
Gashler, Mike
Abstract
In this paper, we prove that the three-dimensional abstract Tile Assembly Model (3DaTAM) is intrinsically universal. This means that there is a universal tile set in the 3DaTAM which can be used to simulate any 3DaTAM system. This result adds to a body of work on the intrinsic universality of models of self-assembly, and is specifically motivated by a result in FOCS 2016 showing that any intrinsically universal tile set for the 2DaTAM requires nondeterminism (i.e. undirectedness) even when simulating directed systems. To prove our result we have not only designed, but also fully implemented what we believe to be the first intrinsically universal tile set which has been implemented and simulated in any tile assembly model, and have made it and a simulator which can display it freely available.
Keywords
self-assembly, simulation, universal, complexity, abstract Tile Assembly System
Citation
Koch, A., Hader, D., & Patitz, M. J. (2018). The 3D abstract Tile Assembly Model is Intrinsically Universal. Computer Science and Computer Engineering Undergraduate Honors Theses Retrieved from https://scholarworks.uark.edu/csceuht/59