What are Keyed functions? (Not Hash) I hope this question is not too obvious, but I came across this paper about PRF, and at some point it writes:

"Let $\mathcal{F}:=\{F_s\}_{s∈S}$ be a family of keyed functions, where each function $F_s$ maps ${\{0, 1\}}^{\ell_1}$ to ${\{0, 1\}}^{\ell_2}$."

What is this meaning of keyed function? What is $S$ in this example?

Thank you!
In the question, each function $F_s$ is transforming an $l_1$-bit bitstring into an $l_2$-bit bitstring.

I read $\mathcal{F}$ being "a family of keyed functions" as meaning that we can re-express all the $F_s$ (that is $\mathcal{F}$) as a single function $F$ with an extra (say, first) argument $K$ in $\{0,1\}^k$ designated the key, and one such key $K_s$ for each $s$ in $S$, such that $\forall x\in{\{0, 1\}^{\ell_1}}, F_s(x)=F(K_s,x)$.

Alternatively, we could have $K_s=s$, and the first argument of $F$ coming from $S$ (that would be the keyspace) rather than some $\{0,1\}^k$. The context should tell.

Addition: That use of "a family of keyed functions" is at least ambiguous and uncommon as far as I can tell. The answer is trying to make sense out of it, but is far from an endorsement.