Theses and Dissertations

Date of Award


Document Type


Degree Name

Master of Science (MS)


Computer Science

First Advisor

Dr. Tim Wylie

Second Advisor

Dr. Robert Schweller

Third Advisor

Dr. Zhixiang Chen


Algorithmic Self Assembly is a well studied field in theoretical computer science motivated by the analogous real world phenomenon of DNA self assembly, as well as the emergence of nanoscale technology. Abstract mathematical models of self assembly such as the Two Handed Assembly model (2HAM) allow us to formally study the computational capabilities of self assembly. The 2HAM is one of the most thoroughly studied models of self assembly, and thus in this paper we study generalizations of this model. The Staged Tile Assembly model captures the behavior of being able to separate assembly processes and combine their outputs at a later time. The k-Handed Assembly Model relaxes the restriction of the 2HAM that only two assemblies can combine in one assembly step. The 2HAM with prebuilt assemblies considers the idea that you can start your assembly process with some prebuilt structures. These generalizations relax some rules of the 2HAM, in ways which reflect real world self assembly mechanics and capabilities. We investigate the complexity of verification problems in these new models, such as the problem of verifying whether a system produces a specified assembly (Producibility), and verifying whether a system uniquely assembles a specified assembly (Unique Assembly Verification). We show that these generalizations introduce a high amount of intractability to these verification problems.


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