@inproceedings{CDM-The-Arithmetic-Complexity-Of-Tensor-Contractions,
Title = {The arithmetic complexity of tensor contractions},
Author = {Florent Capelli and Arnaud Durand and Stefan Mengel},
Booktitle = {Proceedings Symposium on Theoretical Aspects of Computer Science (STACS) 2013},
Year = {2013},
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.},
Url = {http://arxiv.org/abs/1209.4865},
Url2 = {http://drops.dagstuhl.de/opus/volltexte/2013/3948/},
Reviewed = {True}
}