It is widely believed that like Open Question 1, Open Question 2 has an affirmative answer. [24] This in turn suggests that problems which are known to be in the class \(\textbf{NP} \cap \textbf{coNP}\) are unlikely to be \(\textbf{NP}\)-complete (and by symmetric considerations, also unlikely to be \(\textbf{coNP}\)-complete). This class consists of those problems \(X\) which possess polynomial sized certificates for demonstrating both membership and non-membership. It is easy to see that \(\