2009/03/10 by David Doty, Doty, David, Matthew J Patitz +3
Computer Science · #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #cs.DM
paper · pdf · doi:10.48550/arxiv.0903.1857
10 page conference submission with additional technical appendix containing proofs
arxiv created 2009/03/10 · arxiv updated 2009/12/01
We prove that if a set X ⊆ \Z2 weakly self-assembles at temperature 1 in a deterministic tile assembly system satisfying a natural condition known as pumpability, then X is a finite union of semi-doubly periodic sets. This shows that only the most simple of infinite shapes and patterns can be constructed using pumpable temperature 1 tile assembly systems, and gives evidence for the thesis that temperature 2 or higher is required to carry out general-purpose computation in a tile assembly system. Finally, we show that general-purpose computation is possible at temperature 1 if negative glue strengths are allowed in the tile assembly model.