Berg and Ulfberg and Amano and Maruoka have used CNF-DNF-approximators to prove exponential lower bounds for the monotone network complexity of the clique function and of Andreev’s function. We show that these approximators can be used to prove the same lower bound for their non-monotone network complexity. This implies P not equal NP.
More background at: The P-versus-NP page
This page collects links around papers that try to settle the “P versus NP” question (in either way). Here are some links that explain/discuss this question: