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Circuits arithmétiques et calculs tensoriels

Part of: Computability and recursion theory

Published online by Cambridge University Press:  07 October 2008

Guillaume Malod
Guillaume Malod
Affiliation:
Institut de mathématiques, University of Mons-Hainaut, 20, Place du Parc, 7000 Mons, Belgium
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Abstract

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.

Keywords

Valiant's theoryarithmetic circuitstensor calculuscomplexity classes

MSC classification

Secondary: 03D15: Complexity of computation (including implicit computational complexity) 03D30: Other degrees and reducibilities
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 7 , Issue 4 , October 2008 , pp. 869 - 893
Copyright
Copyright © Cambridge University Press 2008

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