Razborov and Rudich have shown that so-called natural proofs are not useful for separating P from NP unless hard pseudorandomnumber generators do not exist. This famous result is widely regarded as a serious barrier to proving strong lower bounds in circuit complexity theory. By definition, a natural combinatorial property satisfies two conditions, constructivity and largeness. Our main result is that if the largeness condition is weakened slightly, then not only does the Razborov
Alexander A. Razborov, Steven Rudich