  We show that weak-coupled two-dimensional dilaton gravity on Anti-de Sitter
space can be described by the dynamics of an open string. Neumann and Dirichlet
boundary conditions for the string lead to two different realizations of the
Anti-de Sitter/Conformal Field Theory correspondence. In particular, in the
Dirichlet case the thermodynamical entropy of two-dimensional black holes can
be exactly reproduced by counting the string states.
