Counting Complexity Classes for Numeric Computations. III: Complex Projective Sets

Authors:
Peter Bürgisser;Felipe Cucker;Martin Lotz
Affiliations:
Deptartment of Mathematics, University of Paderborn, D-33095 Paderborn, Germany;Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong;Deptartment of Mathematics, University of Paderborn, D-33095 Paderborn, Germany
Venue:
Foundations of Computational Mathematics
Year:
2005

Citing 0
Cited 4

Counting complexity classes for numeric computations II: algebraic and semialgebraic sets

Journal of Complexity
Differential forms in computational algebraic geometry

Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Counting complexity classes for numeric computations II: Algebraic and semialgebraic sets

Journal of Complexity
Optimization and approximation problems related to polynomial system solving

CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers

Quantified Score

Hi-index	0.00

Visualization

Abstract

In [8] counting complexity classes #PR and #PC in the Blum-Shub-Smale (BSS) setting of computations over the real and complex numbers, respectively, were introduced. One of the main results of [8] is that the problem to compute the Euler characteristic of a semialgebraic set is complete in the class FPR#PR. In this paper, we prove that the corresponding result is true over C, namely that the computation of the Euler characteristic of an affine or projective complex variety is complete in the class FPC#PC. We also obtain a corresponding completeness result for the Turing model.