Lower Bounds Are Not Easier over the Reals: Inside PH

  • Hervé Fournier
  • Pascal Koiran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1853)


We prove that all NP problems over the reals with addition and order can be solved in polynomial time with the help of a boolean NP oracle. As a consequence, the “P = NP?” question over the reals with addition and order is equivalent to the classical question. For the reals with addition and equality only, the situation is quite different since P is known to be different from NP. Nevertheless, we prove similar transfer theorems for the polynomial hierarchy.


Polynomial Time Turing Machine Polynomial Size Polynomial Hierarchy Transfer Theorem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Hervé Fournier
    • 1
  • Pascal Koiran
    • 1
  1. 1.Laboratoire de l’Informatique du ParallélismeEcole Normale Supérieure de LyonLyon Cedex 07France

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