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2012 IEEE 27th Conference on Computational Complexity (2012)
Porto Portugal
June 26, 2012 to June 29, 2012
ISSN: 1093-0159
ISBN: 978-0-7695-4708-4
pp: 224-234
ABSTRACT
We prove that an associative algebra $A$ has minimal rank if and only if the Alder -- Strassen bound is also tight for the multiplicative complexity of $A$, that is, the multiplicative complexity of $A$ is $2 \dim A - t_A$ where $t_A$ denotes the number of maximal two sided ideals of $A$. This generalizes a result by E. Feig who proved this for division algebras. Furthermore, we show that if $A$ is local or super basic, then every optimal quadratic computation for $A$ is almost bilinear.
INDEX TERMS
associative algebra, algebraic complexity theory, complexity of bilinear problems
CITATION

"Algebras of Minimal Multiplicative Complexity," 2012 IEEE 27th Conference on Computational Complexity(CCC), Porto Portugal, 2012, pp. 224-234.
doi:10.1109/CCC.2012.13
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