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FSTTCS
2006
Springer
14 years 7 days ago
Self-assemblying Classes of Shapes with a Minimum Number of Tiles, and in Optimal Time
Abstract. In this paper we construct fixed finite tile systems that assemble into particular classes of shapes. Moreover, given an arbitrary n, we show how to calculate the tile co...
Florent Becker, Ivan Rapaport, Eric Rémila
EJC
2007
13 years 8 months ago
Complexity of cutting words on regular tilings
: We show that the complexity of a cutting word u in a regular tiling by a polyomino Q is equal to Pn(u) = (p+q−1)n+1 for all n ≥ 0, where Pn(u) counts the number of distinct f...
Pascal Hubert, Laurent Vuillon
UPP
2004
Springer
14 years 1 months ago
Design, Simulation, and Experimental Demonstration of Self-assembled DNA Nanostructures and Motors
Self-assembly is the spontaneous self-ordering of substructures into superstructures driven by the selective affinity of the substructures. DNA provides a molecular scale material...
John H. Reif, Thomas H. LaBean, Sudheer Sahu, Hao ...
STACS
2007
Springer
14 years 2 months ago
On the Complexity of Unary Tiling-Recognizable Picture Languages
Abstract. We give a characterization, in terms of computational complexity, of the family Rec1 of the unary picture languages that are tiling recognizable. We introduce quasi-unary...
Alberto Bertoni, Massimiliano Goldwurm, Violetta L...
FOCS
2009
IEEE
14 years 3 months ago
The Quantum and Classical Complexity of Translationally Invariant Tiling and Hamiltonian Problems
— We study the complexity of a class of problems involving satisfying constraints which remain the same under translations in one or more spatial directions. In this paper, we sh...
Daniel Gottesman, Sandy Irani