In the SATPLAN algorithm in Figure 11.15, each call to the satisfiability algorithm asserts a goal gT, where T ranges from 0 to T,,,. Suppose instead that the satisfiability algorithm is called only once, with the goal go V g1 V . . . V gTmax.

a. Will this always return a plan if one exists with length less than or equal to Tmax?

b. Does this approach introduce any new spurious "solutions"?

c. Discuss how one might modify a satisfiability algorithm such as WALKSAT so that it finds short solutions (if they exist) when given a disjunctive goal of this form.