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Real quantifier elimination is doubly exponential. (English) Zbl 0663.03015
The authors show that quantifier elimination over the first-order theory of real-closed fields can require doubly-exponential space (and hence time) and show that this doubly-exponential behaviour is intrinsic to the problem. This result has already been proved by Weispfenning by a completely different method in 1985, but the method of the paper is of independent interest.
Reviewer: Li Xiang

##### MSC:
 03C10 Quantifier elimination and related topics 68Q25 Analysis of algorithms and problem complexity 12L05 Decidability related to field theory 68W30 Symbolic computation and algebraic computation 12D99 Real and complex fields
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##### References:
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