# 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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