Some algebraic and geometric computations in PSPACE

@inproceedings{Canny1988SomeAA,
  title={Some algebraic and geometric computations in PSPACE},
  author={John F. Canny},
  booktitle={Symposium on the Theory of Computing},
  year={1988}
}
  • J. Canny
  • Published in
    Symposium on the Theory of…
    1988
  • Mathematics
We give a PSPACE algorithm for determining the signs of multivariate polynomials at the common zeros of a system of polynomial equations. One of the consequences of this result is that the “Generalized Movers' Problem” in robotics drops from EXPTIME into PSPACE, and is therefore PSPACE-complete by a previous hardness result [Rei]. We also show that the existential theory of the real numbers can be decided in PSPACE. Other geometric problems that also drop into PSPACE include the 3-d Euclidean… 

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