Journal of Complexity
Two P-complete problems in the theory of the reals
Journal of Complexity
Computing over the reals with addition and order
Selected papers of the workshop on Continuous algorithms and complexity
Computing over the reals with addition and order: higher complexity classes
Journal of Complexity
Generalized knapsack problems and fixed degree separations
Theoretical Computer Science
On the Power of Real Turing Machines over Binary Inputs
SIAM Journal on Computing
A weak version of the Blum, Shub, and Smale model
Journal of Computer and System Sciences - Special issue: dedicated to the memory of Paris Kanellakis
Complexity and real computation
Complexity and real computation
The real dimension problem is NPR -complete
Journal of Complexity
On the Complexity of Some Problems for the Blum, Shub & Smale Model
LATIN '92 Proceedings of the 1st Latin American Symposium on Theoretical Informatics
Counting Complexity Classes for Numeric Computations I: Semilinear Sets
SIAM Journal on Computing
Implicit Complexity over an Arbitrary Structure: Sequential and Parallel Polynomial Time
Journal of Logic and Computation
On the Complexity of Numerical Analysis
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
The complexity of semilinear problems in succinct representation
Computational Complexity
Hi-index | 0.00 |
We define new complexity classes in the Blum-Shub-Smale theory of computation over the reals, in the spirit of the polynomial hierarchy, with the help of infinitesimal and generic quantifiers. Basic topological properties of semialgebraic sets like boundedness, closedness, compactness, as well as the continuity of semialgebraic functions are shown to be complete in these new classes. All attempts to classify the complexity of these problems in terms of the previously studied complexity classes have failed. We also obtain completeness results in the Turing model for the corresponding discrete problems. In this setting, it turns out that infinitesimal and generic quantifiers can be eliminated, so that the relevant complexity classes can be described in terms of usual quantifiers only.