SIAM Journal on Computing
On the Power of Real Turing Machines over Binary Inputs
SIAM Journal on Computing
Complexity and real computation
Complexity and real computation
Topological complexity of the range searching
Journal of Complexity
On Implications between P-NP-Hypotheses: Decision versus Computation in Algebraic Complexity
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Circuits versus Trees in Algebraic Complexity
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Randomized and deterministic algorithms for the dimension of algebraic varieties
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Completeness classes in algebra
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Finding a vector orthogonal to roughly half a collection of vectors
Journal of Complexity
VPSPACE and a transfer theorem over the reals
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Valiant's model: from exponential sums to exponential products
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Characterizing valiant's algebraic complexity classes
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Decision versus evaluation in algebraic complexity
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
Small-space analogues of Valiant's classes
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
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We extend the transfer theorem of [15] to the complex field. That is, we investigate the links between the class VPSPACE of families of polynomials and the Blum-Shub-Smale model of computation over C. Roughly speaking, a family of polynomials is in VPSPACE if its coefficients can be computed in polynomial space. Our main result is that if (uniform, constant-free) VPSPACE families can be evaluated efficiently then the class PARC of decision problems that can be solved in parallel polynomial time over the complex field collapses to PC. As a result, one must first be able to show that there are VPSPACE families which are hard to evaluate in order to separate PC from NPC, or even from PARC.