It is known (1) P \subset P/poly (2) "NP \not\subset P/poly" > "P \neq NP"
However, do we have a proof of: "P \neq NP" > "NP \not\subset P/poly" ?
I.e. is there a world where P \neq NP, but NP \subset P/poly?
Thanks!
It is known (1) P \subset P/poly (2) "NP \not\subset P/poly" > "P \neq NP" However, do we have a proof of: "P \neq NP" > "NP \not\subset P/poly" ? I.e. is there a world where P \neq NP, but NP \subset P/poly? Thanks! 


No, it is unknown whether $P \neq NP \Rightarrow NP \not\subset P/Poly$. However, one may show that if $NP \subset P/Poly$ then the polynomial hierarchy collapses on the second level, what is rather unlikely. 


There are oracles relative to which $P\neq NP$ but $NP\subseteq P/poly$. 

