## Parallel Evaluation of Arithmetic Circuits (1996)

Venue: | Theoretical Computer Science |

Citations: | 2 - 0 self |

### BibTeX

@ARTICLE{Revol96parallelevaluation,

author = {Nathalie Revol and Jean-louis Roch},

title = {Parallel Evaluation of Arithmetic Circuits},

journal = {Theoretical Computer Science},

year = {1996},

pages = {162--133}

}

### OpenURL

### Abstract

this paper, a generic algorithm designed for the parallel evaluation of arithmetic circuits is given. This algorithm can be used in the domain of VLSI design, in order to get tight upper bounds on the computing time of a circuit. It can also be used in automatic parallelization of numerical programs, as a guide for the detection of some predefinite schemes such as dot-products or reductions. More generally, the (theoretical) algorithm presented in section 2 evaluates very quickly arithmetic straight-line programs, and its evaluation time serves as a good upper bound. This algorithm generalizes Miller, Ramachandran and Kaltofen's algorithm [18] in the sense it deals with a great variety of algebraic structures: semi-rings, rings or lattices. Our contribution resides on the one hand in a new bound for the evaluation of circuits over lattices, which improves previous results [19], and on the other hand in the unified formulation for the evaluation algorithm. This algorithm runs in

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Citation Context ...d in section 2 evaluates very quickly arithmetic straight-line programs, and its evaluation time serves as a good upper bound. This algorithm generalizes Miller, Ramachandran and Kaltofen's algorithm =-=[18]-=- in the sense it deals with a great variety of algebraic structures: semi-rings, rings or lattices. Our contribution resides on the one hand in a new bound for the evaluation of circuits over lattices... |

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Citation Context ...t variety of algebraic structures: semi-rings, rings or lattices. Our contribution resides on the one hand in a new bound for the evaluation of circuits over lattices, which improves previous results =-=[19], and on t-=-he other hand in the unified formulation for the evaluation algorithm. This algorithm runs in O(min(log n + log d) log n; (h a + log n) log n)) parallel time, d being the "algebraic degree" ... |

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