Two-matrix model and c = 1 string theory

We show that the most general two-matrix model with bilinear coupling underlies c = 1 string theory. More precisely we prove that W1+∞ constraints, a subset of the correlation functions and the integrable hierarchy charcterizing such two-matrix model, correspond exactly to the W1+∞ constraints, to the discrete tachyon correlation functions and to the integrable hierarchy of the c = 1 string theory.