  We associate to each discrete partial dynamical system a universal C*-algebra
generated by partial isometries satisfying relations given by a Boolean algebra
connected to the discrete partial dynamical system in question. We show that
for symbolic dynamical systems like one-sided and two-sided shift spaces and
topological Markov chains with an arbitrary state space the C*-algebras usually
associated to them, can be obtained in this way.
  As a consequence of this, we will be able to show that for two-sided shift
spaces having a certain property, the crossed product of the two-sided shift
space is a quotient of the C*-algebra associated to the corresponding one-sided
shift space.
