Approximation algorithms for NP-hard problems
Complexity and real computation
Complexity and real computation
Counting problems over the reals
Theoretical Computer Science
Computable analysis: an introduction
Computable analysis: an introduction
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Counting Complexity Classes for Numeric Computations I: Semilinear Sets
SIAM Journal on Computing
Counting Complexity Classes for Numeric Computations. III: Complex Projective Sets
Foundations of Computational Mathematics
Transparent Long Proofs: A First PCP Theorem for NPR
Foundations of Computational Mathematics
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Some Relations between Approximation Problems and PCPs over the Real Numbers
Theory of Computing Systems
Algebraic Complexity Theory
Computing minimal multi-homogeneous bézout numbers is hard
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
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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.