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**1 - 1**of**1**### Notes on Complexity Theory Last updated: December, 2011

"... Recall that one motivation for studying non-uniform computation is the hope that it might be easier to prove lower bounds in that setting. (This is somewhat paradoxical, as non-uniform algorithms are more powerful than uniform algorithms; nevertheless, since circuits are more “combinatorial” in natu ..."

Abstract
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Recall that one motivation for studying non-uniform computation is the hope that it might be easier to prove lower bounds in that setting. (This is somewhat paradoxical, as non-uniform algorithms are more powerful than uniform algorithms; nevertheless, since circuits are more “combinatorial” in nature than uniform algorithms, there may still be justification for such hope.) The ultimate goal here would be to prove that N P ̸ ⊂ P /poly, which would imply P ̸ = N P. Unfortunately, after over two decades of attempts we are unable to prove anything close to this. Here, we show one example of a lower bound that we have been able to prove; we then discuss one “barrier ” that partly explains why we have been unable to prove stronger bounds.