Intrinsic Universality in Self-Assembly

We show that the Tile Assembly Model exhibits a strong notion of universality where the goal is to give a single tile assembly system that simulates the behavior of any other tile assembly system. We give a tile assembly system that is capable of simulating a very wide class of tile systems, including itself. Specifically, we give a tile set that simulates the assembly of any tile assembly system in a class of systems that we call locally consistent: each tile binds with exactly the strength needed to stay attached, and that there are no glue mismatches between tiles in any produced assembly. Our construction is reminiscent of the studies of intrinsic universality of cellular automata by Ollinger and others, in the sense that our simulation of a tile system T by a tile system U represents each tile in an assembly produced by T by a c × c block of tiles in U, where c is a constant depending on T but not on the size of the assembly T produces (which may in fact be infinite). Also, ou...

• Type: Conference
• Year: 2010
• Where: STACS
• Authors: David Doty, Jack H. Lutz, Matthew J. Patitz, Scott M. Summers, Damien Woods
• Keywords: STACS 2010, Theoretical Computer Science, Tile Assembly, Tile Assembly Model, Tile Assembly Systems