  In this paper we show how S-duality of type IIB superstrings leads to an
S-duality relating A and B model topological strings on the same Calabi-Yau as
had been conjectured recently: D-instantons of the B-model correspond to
A-model perturbative amplitudes and D-instantons of the A-model capture
perturbative B-model amplitudes.
  Moreover this confirms the existence of new branes in the two models.
  As an application we explain the recent results concerning A-model
topological strings on Calabi-Yau and its equivalence to the statistical
mechanical model of melting crystal.
