Optimization and approximation problems related
to polynomial system solving
In: Computability in Europe 2006 : Logical Approaches to Computational Barriers, 30 June - 05 July 2006, Swansea.
We outline some current work in real number complexity
theory with a focus on own results. The topics discussed
are all located in the area of
polynomial system solving. First, we concentrate on a combinatorial
optimization problem related to homotopy methods for solving
numerically generic polynomial systems. Then,
approximation problems are discussed in relation with Probabilistically
Checkable Proofs over the real numbers.