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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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Reference request: Proof theory in $W_1^1$

Buss defined $V_2^1$​ as a second-order bounded arithmetic corresponding to $\mathsf{PSPACE}$. Later, Skelley introduced $W_1^1$​, a third-order bounded arithmetic of $\mathsf{PSPACE}$. Since the ques …