Guillaume Lagarde, Guillaume Malod

In the setting of non-commutative arithmetic computations, we define a class of circuits that gener-

alize algebraic branching programs (ABP). This model is called unambiguous because it captures the

polynomials in which all monomials are computed in a similar way (that is, all the parse trees are iso-

morphic).

We ...
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Markus BlĂ¤ser, Christian Ikenmeyer, Meena Mahajan, Anurag Pandey, Nitin Saurabh

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 ... more >>>