### Some articles on *proof, proofs, natural proof, natural, natural proofs*:

... related to the P = NP problem has been in showing that existing

**proof**techniques are not powerful enough to answer the question, thus suggesting that novel ... evidence for the difficulty of the problem, essentially all known

**proof**techniques in computational complexity theory fall into one of the following classifications, each of which ... Most

**proofs**(especially classical ones) apply uniformly in a world with oracles regardless of what the oracle does ...

... In computational complexity theory, a

**natural proof**is a certain kind of

**proof**establishing that one complexity class differs from another one ... While these

**proofs**are in some sense "

**natural**", it can be shown (assuming a widely believed conjecture on the existence of pseudorandom functions) that no such

**proof**can ... The notion of

**natural proofs**was introduced by Alexander Razborov and Steven Rudich in their article

**Natural proofs**, first presented in 1994, and later published in 1997, for ...

### Famous quotes containing the words proofs and/or natural:

“A man’s women folk, whatever their outward show of respect for his merit and authority, always regard him secretly as an ass, and with something akin to pity. His most gaudy sayings and doings seldom deceive them; they see the actual man within, and know him for a shallow and pathetic fellow. In this fact, perhaps, lies one of the best *proofs* of feminine intelligence, or, as the common phrase makes it, feminine intuition.”

—H.L. (Henry Lewis)

“In my state, on the basis of the separate but equal doctrine, we have made enormous strides over the years in the education of both races. Personally, I think it would have been sounder judgment to allow that progress to continue through the process of *natural* evolution. However, there is no point crying about spilt milk.”

—Lyndon Baines Johnson (1908–1973)