### Abstract

This paper extends the stochastic analysis of self assembly in DNA-based computation. The new analysis models an error-correcting technique called pulsing which is analogous to checkpointing in computer operation. The model is couched in terms of the well-known tiling models of DNA-based computation and focuses on the calculation of computation times, in particular the times to self assemble rectangular structures. Explicit asymptotic results are found for small error rates q, and exploit the connection between these times and the classical Hammersley process. Specifically, it is found that the expected number of pulsing stages needed to complete the self assembly of an N × N square lattice is asymptotically 2N √q as N → ∞ within a suitable scaling. Simulation studies are presented which yield performance under more general assumptions.

Original language | English (US) |
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Title of host publication | DNA Computing - 11th International Workshop on DNA Computing, DNA11, Revised Selected Papers |

Pages | 1-11 |

Number of pages | 11 |

Volume | 3892 LNCS |

DOIs | |

State | Published - 2006 |

Event | 11th International Workshop on DNA Computing, DNA11 - London, ON, Canada Duration: Jun 6 2005 → Jun 9 2005 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 3892 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 11th International Workshop on DNA Computing, DNA11 |
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Country | Canada |

City | London, ON |

Period | 6/6/05 → 6/9/05 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*DNA Computing - 11th International Workshop on DNA Computing, DNA11, Revised Selected Papers*(Vol. 3892 LNCS, pp. 1-11). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3892 LNCS). https://doi.org/10.1007/11753681_1

**Self-correcting self-assembly : Growth models and the hammersley process.** / Baryshnikov, Yuliy; Coffman, Ed; Seeman, Nadrian; Yimwadsana, Teddy.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*DNA Computing - 11th International Workshop on DNA Computing, DNA11, Revised Selected Papers.*vol. 3892 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3892 LNCS, pp. 1-11, 11th International Workshop on DNA Computing, DNA11, London, ON, Canada, 6/6/05. https://doi.org/10.1007/11753681_1

}

TY - GEN

T1 - Self-correcting self-assembly

T2 - Growth models and the hammersley process

AU - Baryshnikov, Yuliy

AU - Coffman, Ed

AU - Seeman, Nadrian

AU - Yimwadsana, Teddy

PY - 2006

Y1 - 2006

N2 - This paper extends the stochastic analysis of self assembly in DNA-based computation. The new analysis models an error-correcting technique called pulsing which is analogous to checkpointing in computer operation. The model is couched in terms of the well-known tiling models of DNA-based computation and focuses on the calculation of computation times, in particular the times to self assemble rectangular structures. Explicit asymptotic results are found for small error rates q, and exploit the connection between these times and the classical Hammersley process. Specifically, it is found that the expected number of pulsing stages needed to complete the self assembly of an N × N square lattice is asymptotically 2N √q as N → ∞ within a suitable scaling. Simulation studies are presented which yield performance under more general assumptions.

AB - This paper extends the stochastic analysis of self assembly in DNA-based computation. The new analysis models an error-correcting technique called pulsing which is analogous to checkpointing in computer operation. The model is couched in terms of the well-known tiling models of DNA-based computation and focuses on the calculation of computation times, in particular the times to self assemble rectangular structures. Explicit asymptotic results are found for small error rates q, and exploit the connection between these times and the classical Hammersley process. Specifically, it is found that the expected number of pulsing stages needed to complete the self assembly of an N × N square lattice is asymptotically 2N √q as N → ∞ within a suitable scaling. Simulation studies are presented which yield performance under more general assumptions.

UR - http://www.scopus.com/inward/record.url?scp=33745753535&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745753535&partnerID=8YFLogxK

U2 - 10.1007/11753681_1

DO - 10.1007/11753681_1

M3 - Conference contribution

SN - 3540341617

SN - 9783540341611

VL - 3892 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 1

EP - 11

BT - DNA Computing - 11th International Workshop on DNA Computing, DNA11, Revised Selected Papers

ER -