Exponential replication of patterns in the Signal Tile Assembly Model and experimental non-deterministic assembly of lines in the Probabilistic Tile Assembly Model

Authors

Alexandra B. Keenan, University of Texas-Pan American

Date of Award

5-2014

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Computer Science

First Advisor

Dr. Robert Schweller

Second Advisor

Dr. Zhixiang Chen

Third Advisor

Dr. Bin Fu

Abstract

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.

Comments

Copyright 2014 Alexandra B. Keenan. All Rights Reserved.

https://www.proquest.com/dissertations-theses/exponential-replication-patterns-signal-tile/docview/1560676550/se-2

Granting Institution

University of Texas-Pan American