Application of high-order hopfield neural networks to the solution of diophantine equations

  • G. Joya
  • M. A. Atencia
  • F. Sandoval
Part of the Lecture Notes in Computer Science book series (LNCS, volume 540)


Hopfield and Tank network with high-order weights is applied to the solution of algebraic problems. Particularly, to the search of positive integer solution of a diophantine equation. The chosen representation avoids using all the possible connections among neurons, so reducing one of the most serious problems of high order: combinatorial growing of connections. The energy function is found to be polynomial of order 2n-1 where n is the order of the equation. Although each network is problem-specific, the building process may be extended to other similar problems without any difficulty.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • G. Joya
    • 1
  • M. A. Atencia
    • 1
  • F. Sandoval
    • 2
  1. 1.Dpto. de Arquitectura y Tecnología de Computadores y ElectrónicaUniversidad de MálagaMálagaSpain
  2. 2.Dpto. de Tecnología ElectrónicaUniversidad de MálagaMálagaSpain

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