The Arithmetic Complexity of Tensor Contraction

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 V P , the class of polynomial families efficiently computable by arithmetic circuits. This gives a natural and robust ch...

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Veröffentlicht in:Theory of computing systems Jg. 58; H. 4; S. 506 - 527
Hauptverfasser: Capelli, Florent, Durand, Arnaud, Mengel, Stefan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.05.2016
Springer Nature B.V
Springer Verlag
Schlagworte:
Algebra
Arithmetic
Boolean
Calculus
Circuits
Complexity
Computational Complexity
Computer Science
Mathematical analysis
Polynomials
Studies
Tensors
Theory of Computation
Tensor calculus
Algebraic complexity
Arithmetic circuits
ISSN:1432-4350, 1433-0490
Online-Zugang:Volltext
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Zusammenfassung: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 V P , 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.
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ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-015-9630-8