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Abstract

We show lower bounds for depth of arithmetic networks over algebraically closed fields, real closed fields and the field of the rationals. The parameters used are either the degree or the number of connected components. These lower bounds allow us to show the inefficiency of arithmetic networks to parallelize several natural problems. For instance, we show a √n lower bound for parallel time of the Knapsack problem over the reals and also that the computation of the “integer part” is not well parallelizable by arithmetic networks. Over the rationals we obtain results of similar order and that the Knapsack has an √n lower bound for the parallel time measured by networks. A simply exponential lower bound for the parallel time of quantifier elimination is also shown. Finally, separations among classesP K andNC K are available for fieldsK in the above cases.

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Dedicated to the Memory of Mario Raimondo

Partially supported by DGICyT PB 89/0379 and “POSSO”, ESPRIT-BRA 6846

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Montaña, J.L., Pardo, L.M. Lower bounds for arithmetic networks. AAECC 4, 1–24 (1993). https://doi.org/10.1007/BF01270397

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  • DOI: https://doi.org/10.1007/BF01270397

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