Note that this definition treats accepting and rejecting computations asymmetrically. For if \(x \in X\), some of \(N\)’s computation sequences starting from \(C_0(x)\) may still lead to rejecting states as long as it least one leads to an accepting state. On the other hand, if \(x \not\in X\), then all of \(N\)’s computations from \(C_0(x)\) are required to lead to rejecting states.