Since \(\sc{BHP}\) is \(\textbf{NP}\)-complete, it follows from the closure of \(\textbf{NP}\) under \(\leq_P\) that this problem is in \(\textbf{P}\) only if \(\textbf{P} = \textbf{NP}\). Since this is widely thought not to be the case, this provides some evidence that \(\sc{BHP}\) is an intrinsically difficult computational problem. But since \(\sc{BHP}\) is closely related to the model of computation \(\mathfrak{N}\) itself this may appear to be of little practical significance. It is thus of considerably more interest that a wide range of seemingly unrelated problems originating in many different areas of mathematics are also \(\textbf{NP}\)-complete.