Title: Correspondence Theorem between Holomorphic Discs and Tropical Discs on K3 Surfaces,
Abstract: We prove that the open Gromov-Witten invariants on K3 surfaces satisfy the
Kontsevich-Soibelman wall-crossing formula. One one hand, this gives a
geometric interpretation of the slab functions in Gross-Siebert program. On the
other hands, the open Gromov-Witten invariants coincide with the weighted
counting of tropical discs. This is an analog of the corresponding theorem on
toric varieties \cite{M2}\cite{NS} but on compact Calabi-Yau surfaces.