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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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Analogues of P vs. NP in the history of mathematics
The set of theorems in (what now we call) "absolute geometry" and the set of theorems of "euclidean geometry". That is, the history of the parallel postulate. We now know (after Tarski's formalization …