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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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Can $N!$ be computed in less than $\mathcal{O}(N)$ operations?

The thing that you are asking is the required number of integer operations for computing $N!$ starting only from $1$ and $N$, which is usually referred to as the straight-line complexity of $N!$ denot …
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