Let's consider a special case of Quantified 3-SAT in which the underlying Boolean form...

Let's consider a special case of Quantified 3-SAT in which the underlying Boolean formula has no negated variables. Specifically, let Φ(x1,…,xn) be a Boolean formula of the form

C1 ^ C2 ^ … ^ Ck,

where each Ci is a disjunction of three terms. We say Φ is monotone if each term in each clause consists of a nonnegated variable–that is, each term is equal to xb for some i, rather than .

We define Monotone QSAT to be the decision problem

where the formula Φ is monotone.

Do one of the following two things: (a) prove that Monotone QSAT is PSPACE-complete; or (b) give an algorithm to solve arbitrary instances of Monotone QSAT that runs in time polynomial in n. (Note that in (b), the goal is polynomial time, not just polynomial space.)