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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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practical algorithms for np complete problems
I want to add to the other good answers the following interesting article explaining the successful use of SAT solvers in the work of Konev and Lisitsa on the Erdos Discrepancy problem.
http://rjlipt …