Help on Singular feedback functions

Hey guys, good afternoon.

Actually im working in cryptography, and reading a paper i found a notation that i cant understand and i´ve been searching a lot but i can´t find the meaning.

The paper im reading is A Transformation From the Fibonacci to the Galois NLFSRs (Elena Dubrova). On page 3 she says:
“Most NLFSRs considered in this paper have singular feedback functions of type:
fi(x0,x1,…,xn-1) = x(i+1) mod n XOR gi (x0,x1, …, xn-1), where gi:{0,1}^n-1 → {0,1}, i+1 dont belong dep(gi)”.

And here is my question i dont know what does the gi function do? and why it doesnt depend of x(i+1)?

i hope you can help me.

Thank you.