To better understand why Open Questions 3a,b) are also expected to be decided positively, it will be useful to further explore the relationship between \(\textbf{PSPACE}\) and the characterization of \(\textbf{PH}\) in terms of quantifier alternations. To this end, we first show that the problem \(\sc{TQBF}\) may be redefined in terms of a game between a player called Verifier– who can be thought of as attempting to demonstrate that a QBF-formula \(\phi\) is true – and another player called Falsifier– who can be thought of as attempting to demonstrate that \(\phi\) is not true.[29] Supposing that \(\phi\) is of the form \(\exists x_1 \forall x_2 \ldots Q_n \psi\), a play of the verification game for \(\phi\) is defined as follows: