Irreversibility of Structure Tensors of Modules

10/04/2021

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by   Maciej Wojtala, et al.

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Determining the matrix multiplication exponent ω is one of the greatest open problems in theoretical computer science. We show that it is impossible to prove ω = 2 by starting with structure tensors of modules of fixed degree and using arbitrary restrictions. It implies that the same is impossible by starting with 1_A-generic non-diagonal tensors of fixed size with minimal border rank. This generalizes the work of Bläser and Lysikov [3]. Our methods come from both commutative algebra and complexity theory.