The paper studies the noncommutative rank (ncRANK) problem and the noncommutative rational identity testing (RIT) problem. It presents the following key results:
Deterministic NC reduction from multivariate ncRANK to bivariate ncRANK:
Deterministic NC reduction from multivariate RIT to bivariate RIT:
Deterministic NC-Turing reduction from RIT to bivariate ncRANK:
The reductions establish that if bivariate ncRANK has a deterministic NC algorithm, then both multivariate RIT and multivariate ncRANK would also be in deterministic NC.
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by Vikraman Arv... at arxiv.org 04-26-2024
https://arxiv.org/pdf/2404.16382.pdfDeeper Inquiries