# What are some examples of algorithmic applications of noncommutative rational identity testing?

The problem of polynomial identity testing (PIT) is known to be in $$\mathsf{RP}$$, but not known to be in $$\mathsf{P}$$.

The related problem of noncommutative rational identity testing (NCIT) is known to have a deterministic polynomial algorithm.

I've seen many algorithmic applications of PIT, that work by reducing the detection of some combinatorial object (e.g. existence of a Hamiltonian cycle in a graph) to the verification that a polynomial corresponding to that object is nonzero.

Are there any analogous algorithmic applications of NCIT?