### Abstract

Goldschlager first established that a special case of the monotone planar circuit problem can be solved by a Turing machine in O(log^{2}n) space. Subsequently, Dymond and Cook refined the argument and proved that the same class can be evaluated in O(log^{2}n) time with a polynomial number of processors. In this paper, we prove that the general monotone planar circuit value problem can be evaluated in O(log^{4}n) time with a polynomial number of processors, settling an open problem posed by Goldschlager and Parberry.

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

Pages (from-to) | 369-375 |

Number of pages | 7 |

Journal | SIAM Journal on Computing |

Volume | 24 |

Issue number | 2 |

State | Published - Apr 1995 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Applied Mathematics
- Theoretical Computer Science

### Cite this

*SIAM Journal on Computing*,

*24*(2), 369-375.

**NC algorithm for evaluating monotone planar circuits.** / Delcher, A. L.; Kosaraju, S. Rao.

Research output: Contribution to journal › Article

*SIAM Journal on Computing*, vol. 24, no. 2, pp. 369-375.

}

TY - JOUR

T1 - NC algorithm for evaluating monotone planar circuits

AU - Delcher, A. L.

AU - Kosaraju, S. Rao

PY - 1995/4

Y1 - 1995/4

N2 - Goldschlager first established that a special case of the monotone planar circuit problem can be solved by a Turing machine in O(log2n) space. Subsequently, Dymond and Cook refined the argument and proved that the same class can be evaluated in O(log2n) time with a polynomial number of processors. In this paper, we prove that the general monotone planar circuit value problem can be evaluated in O(log4n) time with a polynomial number of processors, settling an open problem posed by Goldschlager and Parberry.

AB - Goldschlager first established that a special case of the monotone planar circuit problem can be solved by a Turing machine in O(log2n) space. Subsequently, Dymond and Cook refined the argument and proved that the same class can be evaluated in O(log2n) time with a polynomial number of processors. In this paper, we prove that the general monotone planar circuit value problem can be evaluated in O(log4n) time with a polynomial number of processors, settling an open problem posed by Goldschlager and Parberry.

UR - http://www.scopus.com/inward/record.url?scp=0029289933&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029289933&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0029289933

VL - 24

SP - 369

EP - 375

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

SN - 0097-5397

IS - 2

ER -