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valiant's theory

Journal of the Institute of Mathematics of Jussieu (1)

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1 results

Circuits arithmétiques et calculs tensoriels
Part of
- Computability and recursion theory
Guillaume Malod
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 7 / Issue 4 / October 2008

Published online by Cambridge University Press:

07 October 2008, pp. 869-893

Print publication:

October 2008
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The classes in Valiant's theory are classes of polynomials defined by arithmetic circuits. We characterize them by different notions of tensor calculus, in the vein of Damm, Holzer and McKenzie. This characterization underlines in particular the role played by properties of parallelization in these classes. We also give a first natural complete sequence for the class VPnb, the analogue of the class P in this context.