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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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Speeding the quadratic sieve with an oracle

If we know the factorization of $N$ then we can take square roots of small numbers that are quadratic residues mod all primes dividing $N$. Knowing a partial factorization of size $M\sim N^\alpha$, sq …
Dror Speiser's user avatar
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Lower Bounds in Theoretical Computer Science

From the wikipedia page of matrix multiplication: Raz (2002) proves a lower bound of $\Omega(m^2\log m)$ for bounded coefficient arithmetic circuits over the real or complex numbers.