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This is a branch that includes: computational complexity theory; complexity classes, NP-completeness and other completeness concepts; oracle analogues of complexity classes; complexity-theoretic computational models; regular languages; context-free languages; Komolgorov Complexity and so on.
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Time functions of non-deterministic Turing machines
Not clear what you're asking, but normally we define complexity classes in terms of asymptotics of N, i.e. log(N), poly(N), exp(N), 2exp(N), etc. That the TM is nondeterministic doesn't change the ov …