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Lower bounds for arithmetic networks II: Sum of Betti numbers

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

We show lower bounds for the parallel complexity of membership problems in semialgebraic sets. Our lower bounds are obtained from the Euler characteristic and the sum of Betti numbers. We remark that these lower bounds are polynomial (an square root) in the sequential lower bounds obtained by Andrew C.C. Yao.

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Authors and Affiliations

  1. Departamento de Matemáticas, Estadistica y Computación. Facultad de Ciencias, Universidad de Cantabria, E-39071, Santander, Spain

    J. E. Morais & Luis M. Pardo

  2. Departamento de Matemáticas e Informática, Universidad Pública de Navarra, Campus de Rosadía. Pamplona, 31006, Navarra, Spain

    J. L. Montaña

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  1. J. L. Montaña
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  2. J. E. Morais
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  3. Luis M. Pardo
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Partially supported by 92-0498-C02-01, PB93-0472-C02-02 and “POSS”, ESPRIT-BRA 6846.

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Montaña, J.L., Morais, J.E. & Pardo, L.M. Lower bounds for arithmetic networks II: Sum of Betti numbers. AAECC 7, 41–51 (1996). https://doi.org/10.1007/BF01613615

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  • DOI: https://doi.org/10.1007/BF01613615

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