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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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votes
Is there a formal notion of what we do when we 'Let X be ...'?
Since you expressly asked for links to La Wik, start with Extension by definitions
The article does not seem to address computational complexity directly, so I'm leaving that issue for other users.