Computing local dimension of a semialgebraic set
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A black box approach to the algebraic set decomposition problem
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On the complexity of diophantine geometry in low dimensions (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
The resultant of an unmixed bivariate system
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Counting complexity classes for numeric computations II: algebraic and semialgebraic sets
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
On the complexity of counting components of algebraic varieties
Journal of Symbolic Computation
VPSPACE and a transfer theorem over the complex field
Theoretical Computer Science
VPSPACE and a transfer theorem over the complex field
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Critical point methods and effective real algebraic geometry: new results and trends
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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We prove old and new results on the complexity of computing the dimension of algebraic varieties. In particular, we show that this problem is NP-complete in the Blum-Shub-Smale model of computation over C, that it admits a s/sup O(1)/D/sup O(n)/ deterministic algorithm, and that for systems with integer coefficients it is in the Arthur-Merlin class under the Generalized Riemann Hypothesis. The first two results are based on a general derandomization argument.