Randomized and Deterministic Algorithms for the Dimension of Algebraic Varieties

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 sO(1)DO(n) deterministic algorithm, and that for systems with integer coe cients it is in the Arthur-Merlin class under the Generalized Riemann Hypothesis. The rst two results are based on a general derandomization argument.

• Type: Conference
• Year: 1997
• Where: FOCS
• Authors: Pascal Koiran
• Keywords: FOCS 1997, General Derandomization Argument, Generalized Riemann Hypothesis, Integer Coe Cients, Theoretical Computer Science