Whether randomness provides practical computational advantage over determinism remains an open problem

As the standard Turing machine model \(\mathfrak{T}\) corresponds to a special case of \(\mathfrak{C}\), it follows that \(\textbf{P} \subseteq \textbf{BPP}\). For a long time, it was also thought that \(\sc{PRIMES}\) might be an example of a problem which was in \(\textbf{BPP}\) but not \(\textbf{P}\).[35] However, we now know that this problem is in \(\textbf{P}\) in virtue of the AKS primality algorithm. At present, not only are there few known candidates for separating these classes, but it