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Algebraic Branching Programs, Border Complexity, and Tangent Spaces
[article]

2020
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arXiv
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pre-print

Nisan showed in 1991 that the width of a smallest noncommutative single-(source,sink) algebraic branching program (ABP) to compute a noncommutative polynomial is given by the ranks of specific matrices. This means that the set of noncommutative polynomials with ABP width complexity at most k is Zariski-closed, an important property in geometric complexity theory. It follows that approximations cannot help to reduce the required ABP width. It was mentioned by Forbes that this result would

arXiv:2003.04834v1
fatcat:xv532a7arjaljbu6znckcsocpm