# The Tile Assembly Model is Intrinsically Universal

@article{Doty2012TheTA, title={The Tile Assembly Model is Intrinsically Universal}, author={D. Doty and J. Lutz and Matthew J. Patitz and Robert T. Schweller and Scott M. Summers and D. Woods}, journal={2012 IEEE 53rd Annual Symposium on Foundations of Computer Science}, year={2012}, pages={302-310} }

We prove that the abstract Tile Assembly Model (aTAM) of nanoscale self-assembly is intrinsically universal. This means that there is a single tile assembly system U that, with proper initialization, simulates any tile assembly system T. The simulation is "intrinsic" in the sense that the self-assembly process carried out by U is exactly that carried out by T, with each tile of T represented by an m × m "super tile" of U. Our construction works for the full aTAM at any temperature, and it… Expand

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#### References

SHOWING 1-10 OF 65 REFERENCES

Reducing tile complexity for self-assembly through temperature programming

- Mathematics, Computer Science
- SODA '06
- 2006

Simulation of Self-Assembly in the Abstract Tile Assembly Model with ISU TAS

- Computer Science
- ArXiv
- 2011

Temperature 1 self-assembly: deterministic assembly in 3D and probabilistic assembly in 2D

- Computer Science, Mathematics
- SODA '11
- 2011

Strong Fault-Tolerance for Self-Assembly with Fuzzy Temperature

- Mathematics, Computer Science
- 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
- 2010

The Undecidability of the Infinite Ribbon Problem: Implications for Computing by Self-Assembly

- Mathematics, Computer Science
- SIAM J. Comput.
- 2009

Toward reliable algorithmic self-assembly of DNA tiles: a fixed-width cellular automaton pattern.

- Chemistry, Medicine
- Nano letters
- 2008

The program-size complexity of self-assembled squares (extended abstract)

- Mathematics, Computer Science
- STOC '00
- 2000