(a) in interrogative sentence - Express confusion or strong doubt
Can + S ....? (about present)
Can + S + have + p.p ....? (about past)
(b) in negative sentence - strong possibility
S + cannot .... (about present)
S + cannot have + p.p .... (about past)
(ex a) Can you think the fact be true?
= I think, it is impossible that the fact is true.
(ex b) He can't have done his homework through all that noise.