  Let $T$ be a matrix whose entries are linear forms over the noncommutative
variables $x_1, x_2, \ldots, x_n$. The noncommutative Edmonds' problem
(NSINGULAR) aims to determine whether $T$ is invertible in the free skew field
generated by $x_1,x_2,\ldots,x_n$. Currently, there are three different
deterministic polynomial-time algorithms to solve this problem: using operator
scaling [Garg, Gurvits, Oliveira, and Wigserdon (2016)], algebraic methods
[Ivanyos, Qiao, and Subrahmanyam (2018)], and convex optimization [Hamada and
Hirai (2021)].
  In this paper, we present a simpler algorithm for the NSINGULAR problem.
While our algorithmic template is similar to the one in Ivanyos et. al.(2018),
it significantly differs in its implementation of the rank increment step.
Instead of computing the limit of a second Wong sequence, we reduce the problem
to the polynomial identity testing (PIT) of noncommutative algebraic branching
programs (ABPs).
  This enables us to bound the bit-complexity of the algorithm over
$\mathbb{Q}$ without requiring special care. Moreover, the rank increment step
can be implemented in quasipolynomial-time even without an explicit description
of the coefficient matrices in $T$. This is possible by exploiting the
connection with the black-box PIT of noncommutative ABPs [Forbes and Shpilka
(2013)].
