Problems still "hard" in the SMP/Referee model with shared randomness?
If A has a pointer (of length $\log n$) to a bit of B (whose input has length $n$), that requires, $\Theta(\log n)$ one-way communication, even with a public-coin. On the other hand, the referee needs $\Theta(n)$ bits to solve the problem, even with a public-coin. Or did I misunderstand something?