For this question we are meant to convert the omega automata

A∀({q, p}, ¬q ∧ ¬p,(Xq ↔ (¬q ∧ ¬a)) ∧ (Xp ↔ (¬p → q)), GFp)

to LO2, can we just use the formula that was given in slide 25 of the predicate logic slides so the answer in LO2 would be

∃q,p. ΘLO2(0, !p&!q )∧ (∀t. ΘLO2(t, ϕR)) ∧ (∀t1.∃t2.t1 < t2 ∧ ΘLO2(t2, GFp ))

where ϕR = (Xq ↔ (¬q ∧ ¬a)) ∧ (Xp ↔ (¬p → q))