Strangely, if we let $S^R$ be the reverse of a reference string S, then the page-fault rate for the OPT algorithm on S is the same as the page-fault rate for the OPT algorithm on $S^R$ . Similarly, the page-fault rate for the LRU algorithm on S is the same as the page-fault rate for the LRU algorithm on $S^R$ .
Can anyone explain why is it true?? The line just before this says - "We can think of this(referring to LRU) strategy as the optimal page-replacement algorithm looking backward in time, rather than forward."
So, shouldn't it be:
page-fault-rate(OPT($S$)) = page-fault-rate(LRU($S^R$))
???