the definition of F as a set of sets sounds incorrect

[adl]

In the formal semantics we have something like this

$F={S_0,S_1,…,S_{m−1}}$ is a finite set of acceptance sets.

where each S_i is a subset of transitions.

I think declaring F as a set is a mistake, because it implicitly implies that all S_i will be different, which is not the case in the format.

I suggest to rewrite this as

$F=(S_0,S_1,…,S_{m−1})$ is a tuple of $m$ acceptance sets.

Do you agree?

[xblahoud]

Tuple sounds fine to me. It naturally comes with the order and indexing the sets. I can't see any advantage of having a set there.

[strejcek]

Or we can say that $F=S_0,S_1,…,S_{m−1}$ is a finite sequence of $m$ acceptance sets.
I like it slightly more than tuples of an arbitrary arity/length.