Theory and Algorithms Commons^™

Computational Complexity Of Determining The Rigidity Of Ftam Assemblies, Ian Perkins

Computer Science and Computer Engineering Undergraduate Honors Theses

In this paper, we discuss a tile-based self-assembly model called the Folding Tile Assembly Model (FTAM). We briefly define what makes the FTAM unique in its ability to have folding 2D tiles. We also discuss the difficulty of determining the computational complexity of certain FTAM properties despite it being simpler for less dynamic models. Specifically, we discuss the property of rigidity in FTAM assemblies by devising a simple definition of rigidity, so that it is easier to determine its complexity. We use a reduction between an assembly and a 3SAT instance along with a series of proofs to give a …