I don't think I understand correctly what it means for a Boolean formula to be reversible. By my current understanding, if a Boolean formula is satisfiable, then there exists a setting of variables such that the formula evaluates to true. If you were to reverse said formula, simply flipping each variable in the setting would also satisfy the reverse formula. You can similarly show that the reverse formula is satisfiable if the original formula. Overall, the reversible formula is satisfiable if and only if the original Boolean expression is. Since the author claims that determining reversibility is NP-complete, I think I'm missing something here.
This is from the paper: On the Complexity of Polyhedral Separability