“…To show that MINTILESET is Σ P 2 -hard, we show that ∃∀CNF-UNSAT is polynomial-time many-one reducible to MINTILESET, where ∃∀CNF-UNSAT is the Σ P 2 -complete language [40,45,50] ∃∀CNF-UNSAT = ϕ ϕ is a true quantified Boolean formula ϕ = ∃x∀y¬φ (x, y), where φ is an unquantified CNF formula with n + m input bits x = x 1 , . .…”