I have a function $F: \{0,1\}^n \to \{0,1\}^n$. Denote by $F_i : \{0,1\}^n \to \{0,1\}$ the $i$th component. I assume that for each $i$, $F_i$ can be written as conjunction of at most $n$ propositional literals (i.e. propositional variables or negated propositional variables). These formulas are known.

I am interested in obtaining the image $F(\{0,1\}^n)$ or it's complement from the syntax of the $F_i$ formulas, which I hope would be faster than enumerating the whole domain.

EDIT: Computing only $|F(\{0,1\}^n)|$ would be also useful to me.

Could anyone give me a hint how to approach such problem?