The arithmetic complexity of tensor contractions
Computational Complexity
2012-09-24 v1
Abstract
We investigate the algebraic complexity of tensor calulus. 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
Cite
@article{arxiv.1209.4865,
title = {The arithmetic complexity of tensor contractions},
author = {Florent Capelli and Arnaud Durand and Stefan Mengel},
journal= {arXiv preprint arXiv:1209.4865},
year = {2012}
}