Papers › Depth-first search for tensor rank and border rank over finite fields
Depth-first search for tensor rank and border rank over finite fields
Jason Yang
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We present an O^*(|𝔽|^((R-n_*)(∑_d n_d)+n_*))-time algorithm for determining whether a tensor of shape n₀×…×n_(D-1) over a finite field 𝔽 has rank ≤R, where n_*:=max_d n_d; we assume without loss of generality that ∀d:n_d≤R. We also extend this problem to its border rank analog, i.e., determining tensor rank over rings of the form 𝔽[x]/(xᴴ), and give an O^*(|𝔽|^(H∑_(1≤r≤R) ∑_d min(r,n_d)))-time algorithm. Both of our algorithms use polynomial space.
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