Theses and Dissertations - UTB/UTPA
Exponential replication of patterns in the Signal Tile Assembly Model and experimental non-deterministic assembly of lines in the Probabilistic Tile Assembly Model
Date of Award
Master of Science (MS)
Dr. Robert Schweller
Dr. Zhixiang Chen
Dr. Bin Fu
We introduce the problem of self-replication of rectangular two-dimensional patterns in the practically motivated Signal Tile Assembly Model (STAM), which is an extension of the aTAM. In the first part of this thesis, we construct an exponential pattern replicator that replicates a two-dimensional input pattern over some fixed alphabet of size ϕ with O(ϕ) tile types, O(ϕ) unique glues, and a signal complexity of O(1). In the second part of this thesis, we use a non-deterministic model of tile assembly to significantly reduce the tile complexity of specified-length linear assemblies, which are a particularly important substructure for building more complicated nanostructures.
University of Texas-Pan American
Copyright 2014 Alexandra B. Keenan. All Rights Reserved.