Separation of complexity classes in Koiran's weak model
Selected papers of the workshop on Continuous algorithms and complexity
On the complexity of quadratic programming in real number models of computation
Selected papers of the workshop on Continuous algorithms and complexity
On the combinatorial and algebraic complexity of quantifier elimination
Journal of the ACM (JACM)
Complexity and real computation
Complexity and real computation
Why does information-based complexity use the real number model?
Theoretical Computer Science - Special issue on computability and complexity in analysis
A weak version of the Blum, Shub and Smale model
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
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Many problems in interval arithmetic in a natural way lead to a quantifier elimination problem over the reals. By studying closer the precise form of the latter we show that in some situations it is possible to obtain a refined complexity analysis of the problem. This is done by structural considerations of the special form of the quantifiers and its implications for the analysis in a real number model of computation. Both can then be used to obtain as well new results in the Turing model. We exemplify our approach by dealing with different versions of the approximation problem for interval functions.