### Abstract

We demonstrate that DNA computers can simulate Boolean circuits with a small overhead. Boolean circuits embody the notion of massively parallel signal processing and are frequently encountered in many parallel algorithms. Many important problems such as sorting, integer arithmetic, and matrix multiplication are known to be computable by small size Boolean circuits much faster than by ordinary sequential digital computers. This paper shows that DNA chemistry allows one to simulate large semi-unbounded fan-in Boolean circuits with a logarithmic slowdown in computation time. Also, for the class NC^{1}, the slowdown can be reduced to a constant. In this algorithm we have encoded the inputs, the Boolean AND gates, and the OR gates to DNA oligonucleotide sequences. We operate on the gates and the inputs by standard molecular techniques of sequence-specific annealing, ligation, separation by size, amplification, sequence-specific cleavage, and detection by size. Additional steps of amplification are not necessary for NC^{1} circuits. The feasibility of the DNA algorithm has been successfully tested on a small circuit by actual biochemical experiments.

Original language | English (US) |
---|---|

Pages (from-to) | 239-250 |

Number of pages | 12 |

Journal | Algorithmica (New York) |

Volume | 25 |

Issue number | 2-3 |

State | Published - 1999 |

Externally published | Yes |

### Fingerprint

### Keywords

- Boolean circuits
- DNA computation
- Parallel computation

### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design
- Software
- Safety, Risk, Reliability and Quality
- Applied Mathematics

### Cite this

*Algorithmica (New York)*,

*25*(2-3), 239-250.

**Simulating Boolean circuits on a DNA computer.** / Ogihara, Mitsunori; Ray, A.

Research output: Contribution to journal › Article

*Algorithmica (New York)*, vol. 25, no. 2-3, pp. 239-250.

}

TY - JOUR

T1 - Simulating Boolean circuits on a DNA computer

AU - Ogihara, Mitsunori

AU - Ray, A.

PY - 1999

Y1 - 1999

N2 - We demonstrate that DNA computers can simulate Boolean circuits with a small overhead. Boolean circuits embody the notion of massively parallel signal processing and are frequently encountered in many parallel algorithms. Many important problems such as sorting, integer arithmetic, and matrix multiplication are known to be computable by small size Boolean circuits much faster than by ordinary sequential digital computers. This paper shows that DNA chemistry allows one to simulate large semi-unbounded fan-in Boolean circuits with a logarithmic slowdown in computation time. Also, for the class NC1, the slowdown can be reduced to a constant. In this algorithm we have encoded the inputs, the Boolean AND gates, and the OR gates to DNA oligonucleotide sequences. We operate on the gates and the inputs by standard molecular techniques of sequence-specific annealing, ligation, separation by size, amplification, sequence-specific cleavage, and detection by size. Additional steps of amplification are not necessary for NC1 circuits. The feasibility of the DNA algorithm has been successfully tested on a small circuit by actual biochemical experiments.

AB - We demonstrate that DNA computers can simulate Boolean circuits with a small overhead. Boolean circuits embody the notion of massively parallel signal processing and are frequently encountered in many parallel algorithms. Many important problems such as sorting, integer arithmetic, and matrix multiplication are known to be computable by small size Boolean circuits much faster than by ordinary sequential digital computers. This paper shows that DNA chemistry allows one to simulate large semi-unbounded fan-in Boolean circuits with a logarithmic slowdown in computation time. Also, for the class NC1, the slowdown can be reduced to a constant. In this algorithm we have encoded the inputs, the Boolean AND gates, and the OR gates to DNA oligonucleotide sequences. We operate on the gates and the inputs by standard molecular techniques of sequence-specific annealing, ligation, separation by size, amplification, sequence-specific cleavage, and detection by size. Additional steps of amplification are not necessary for NC1 circuits. The feasibility of the DNA algorithm has been successfully tested on a small circuit by actual biochemical experiments.

KW - Boolean circuits

KW - DNA computation

KW - Parallel computation

UR - http://www.scopus.com/inward/record.url?scp=0008910229&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0008910229&partnerID=8YFLogxK

M3 - Article

VL - 25

SP - 239

EP - 250

JO - Algorithmica

JF - Algorithmica

SN - 0178-4617

IS - 2-3

ER -