Hilbert's Nullstellensatz Is in the Polynomial Hierarchy

@article{Koiran1996HilbertsNI,
  title={Hilbert's Nullstellensatz Is in the Polynomial Hierarchy},
  author={Pascal Koiran},
  journal={J. Complex.},
  year={1996},
  volume={12},
  pages={273-286}
}
  • P. Koiran
  • Published 30 July 1996
  • Mathematics
  • J. Complex.
We show that if the Generalized Riemann Hypothesis is true, the problem of deciding whether a system of polynomial equations in several complex variables has a solution is in the second level of the polynomial hierarchy. In fact, this problem is in AM, the ``Arthur-Merlin'''' class (recall that $\np \subseteq \am \subseteq \rp^{\tiny \np} \subseteq \Pi_2$). The best previous bound was PSPACE. An earlier version of this paper was distributed as NeuroCOLT Technical Report~96-44. The present paper… 
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