Combinatorial optimization problems in self-assembly
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Algorithmic self-assembly of dna
Algorithmic self-assembly of dna
Complexities for Generalized Models of Self-Assembly
SIAM Journal on Computing
Staged self-assembly: nanomanufacture of arbitrary shapes with O(1) glues
Natural Computing: an international journal
An Almost Totally Universal Tile Set
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Polyomino-Safe DNA Self-assembly via Block Replacement
DNA Computing
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Communication complexity and intrinsic universality in cellular automata
Theoretical Computer Science
Theoretical Computer Science
Bulking II: Classifications of cellular automata
Theoretical Computer Science
Bulking I: An abstract theory of bulking
Theoretical Computer Science
Parallelism and time in hierarchical self-assembly
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
The Tile Assembly Model is Intrinsically Universal
FOCS '12 Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
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In this paper, we study the intrinsic universality of the well-studied Two-Handed Tile Assembly Model (2HAM), in which two "supertile" assemblies, each consisting of one or more unit-square tiles, can fuse together (self-assemble) whenever their total attachment strength is at least the global temperature τ. Our main result is that for all τ′τ, each temperature-τ′ 2HAM tile system cannot simulate at least one temperature-τ 2HAM tile system. This impossibility result proves that the 2HAM is not intrinsically universal, in stark contrast to the simpler abstract Tile Assembly Model which was shown to be intrinsically universal (The tile assembly model is intrinsically universal, FOCS 2012). On the positive side, we prove that, for every fixed temperature τ≥2, temperature-τ 2HAM tile systems are intrinsically universal: for each τ there is a single universal 2HAM tile set U that, when appropriately initialized, is capable of simulating the behavior of any temperature τ 2HAM tile system. As a corollary of these results we find an infinite set of infinite hierarchies of 2HAM systems with strictly increasing power within each hierarchy. Finally, we show how to construct, for each τ, a temperature-τ 2HAM system that simultaneously simulates all temperature-τ 2HAM systems.