The complexity of semilinear problems in succinct representation

Authors:
Peter Bürgisser;Felipe Cucker;Paulin Jacobé Naurois
Affiliations:
Department of Mathematics, University of Paderborn, Paderborn, Germany D-33095;Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong;LORIA, Villers-lès-Nancy Cedex, France 54602
Venue:
Computational Complexity
Year:
2006

Citing 0
Cited 6

On the complexity of deciding connectedness and computing Betti numbers of a complex algebraic variety

Journal of Complexity
Differential forms in computational algebraic geometry

Proceedings of the 2007 international symposium on Symbolic and algebraic computation
On the complexity of counting components of algebraic varieties

Journal of Symbolic Computation
Real Computable Manifolds and Homotopy Groups

UC '09 Proceedings of the 8th International Conference on Unconventional Computation
Exotic quantifiers, complexity classes, and complete problems

ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Computational complexity of kernel-based density-ratio estimation: a condition number analysis

Machine Learning

Quantified Score

Hi-index	0.00

Visualization

Abstract

We prove completeness results for twenty-three problems in semilinear geometry. These results involve semilinear sets given by additive circuits as input data. If arbitrary real constants are allowed in the circuit, the completeness results are for the Blum---Shub---Smale additive model of computation. If, in contrast, the circuit is constant-free, then the completeness results are for the Turing model of computation. One such result, the PNP[log]-completeness of deciding Zariski irreducibility, exhibits for the first time a problem with a geometric nature complete in this class.