Theory of Computing Systems

, Volume 58, Issue 4, pp 506–527 | Cite as

The Arithmetic Complexity of Tensor Contraction

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Abstract

We investigate the algebraic complexity of tensor calculus. We consider a generalization of iterated matrix product to tensors and show that the resulting formulas exactly capture VP, the class of polynomial families efficiently computable by arithmetic circuits. This gives a natural and robust characterization of this complexity class that despite its naturalness is not very well understood so far.

Keywords

Algebraic complexity Arithmetic circuits Tensor calculus 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.IMJ UMR 7586 - LogiqueUniversité Paris DiderotParisFrance
  2. 2.LIX UMR 7161, Ecole PolytechniquePalaiseauFrance

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