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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:
03C10Quantifier elimination and related topics
68Q25Analysis of algorithms and problem complexity
12L05Decidability related to field theory
68W30Symbolic computation and algebraic computation
12D99Real and complex fields