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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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Modular square roots problem which is $NP$ hard
According to the paper NP-complete decision problems for quadratic polynomials (Thm. 2) by K. Manders and L. Adleman the following problem $A$ is NP-complete thus in particular NP-hard:
Given $\alpha, …