This is independent,
!HPF$ INDEPENDENT DO i = 1, n b(i) = b(i) + b(i) END DO
this is not, (dependence on order of execution),
DO i = 1, n b(i) = b(i+1) + b(i) END DO
nor is this,
DO i = 1, n b(i) = b(i-1) + b(i) END DO
however, this is
!HPF$ INDEPENDENT DO i = 1, n a(i) = b(i-1) + b(i) END DO
For more information, click here